That's an interesting question, because, for sure, there are aspects of the stories of the two Dark Lords that closely parallel one another, which almost suggests a familiarity between their Creators (but that's an argument for another day).

The One Ring, as I understand it, and as common knowledge would understand it, was forged under the power of the Dark Lord Sauron for the purposes of (a) ruling the populace of Middle-Earth through its magical influence and (b) link the Dark Lord's spirit and works to the Ring, and thus ensure that while it endured, he endured.

The basic idea of a Horcrux is this (I can't cite a reliable source here, because even tomes such as Magick Moste Evile refuse to describe such Dark Arts): It captures a piece of the soul of the maker in order to achieve immortality. With the Dark Lord Voldemort in particular, Horcruxes appear to exert some influence over people who come into close proximity with said Horcruces (I cite here the example of the interaction between the Diary and the Weasley M*dblood).

In addition, because the Dark Lord Sauron had to pour so much malice and energy into the forging of the One Ring, he was consequentially much weaker when divested of it. This jives well with the apocrypha surrounding Horcruces, which purports that the maker becomes disfigured, or their humanity becomes diminished (whether or not the Dark Lord Sauron was ever considered "human," one cannot deny that this weakening, to one of such power, is tantamount to disfigurement).

Now, methods of destruction. The apocryphal story surrounding the artifact known as the Horcrux argues that it can be destroyed by Fiendfyre, an Uber-destructive substance such as basilisk venom (or a weapon imbued with such a substance), and, in the case of living Horcruces, the Killing Curse. This is where the apocrypha of Horcruces and the One Ring diverge; several examples of the destruction of conventional Horcruces by these means are available (those of the Dark Lord Voldemort, two of which were living), but the One Ring has proven repeatedly that it cannot/could not be destroyed by any means other than the fire in which it was forged. A case could possibly be made for the lava of Orodruin containing some trace amount of Fiendfyre, but I'm not a specialist in Mordoran geology.

All this nattering on leads to one point, which is that, while sufficient evidence exists to argue the point that the One Ring was a Horcrux, in that it tied the spirit and works of the Dark Lord Sauron to the land over which he reigned, there are also sufficient differences in the lore to argue the opposite side. I'm sure more learned scholars than myself could take a much more thorough crack at this question, but, to my eyes, there is no concrete answer, only an apocryphal structure that can be held up to the light for comparison.

Edit: Fixed a typo that caused a canon error.

I would argue that both the One Ring and Voldemort's Horcruxes fall under the broader category of Phylacteries, as defined by Gygax et al. in various editions of the Dungeons & Dragons series of encyclopedias. These volumes speak of the creation of a phylactery as a key component of becoming a Lich, an undead creature of vast intellect and magical ability (although it is unclear whether these traits are a consequence of the process, or a prerequisite).

A phylactery can take many forms, from a collection of magical scrolls within a sealed container to items of jewellery, but in all cases such an item allows the Lich it was created by to be resurrected (although it should be noted they can only be returned to their undead form, not to their pre-Lich state as per a "true" resurrection) after their body is destroyed. Whether the Phylactery contains a fraction of the creator's soul or just allows the soul to be transferred to it in the case of the Lich's "death" is still a point of contention among necromantic scholars, with some arguing that the Lich's soul is contained wholly within the artifact, and that the Lich's body is really just a form of necromantic posession.

In the case of Voldemort, there are no records of whether he was medically alive following the creation of his Horcruxes - indeed, his unnatural face structure and pale complexion after his "resurrection" in Little Hangleton, as well as his total inability to experience compassion, suggests he most likely was not a living human at that point. The fact Voldemort was able to create multiple phylacteries can be seen either as a magical weakness (unable to wholly place his soul in a container) or a strength (able to spread his soul equally between several containers) - such speculation could only be settled if the exact magical nature of phylacteries was known.

In the case of Sauron's Ring, we already know that Sauron was not a mortal being, as he is comparable in nature to the Maiar, having originated as one of the Valar. Whether that means he could not be considered a Lich, as such a being could never be alive or dead (and by extension undead) as defined with regards to the other races of Middle Earth, is debatable. Regardless, the One Ring shares several properties with a Phylactery, most notably the fact it allows the soul of its creator to survive beyond the destruction of their body.

The major difference between a horcrux and the One Ring is that the Horcruxes could be destroyed in several ways, whereas the One Ring was only able to be destroyed in the fires of its creation. This also supports the idea that Voldemort's horcruxes were formed with weaker magic than Sauron's Ring.

Another difference is that Voldemort created his horcruxes with the express desire to survive death, whereas this may be a side effect in the case of the One Ring. The latter was primarily designed to enhance Sauron's innate ability to dominate the minds of others, while no records show Voldemort as becoming more powerful in the presence of his horcruxes. Thus it can be argued that this direct link to the inherent magic of Sauron's being is what caused the phylacteric properties of the Ring, which serves as testament to the incredibly advanced level of magic Sauron was able to wield.

TL;DR - Both are likely similar but different forms of Phylactery, an artifact used by powerful undead to survive death.

In short, no. Sauron was not a human, and thus his spirit is different than that of Men. Furthermore, he forgred himself into the Ring - he did not just make the Ring and put some of his spirit in it.

Furthermore the Ring also held and gave power - horcruxes do not do that.

Consider cross posting to /r/askscience for a more technical discussion on the topic.

Here's the thing. You said "Was the One Ring really just a horcrux." Is it in the same family? Yes. No one's arguing that. As someone who is a magus who studies magic rings, I am telling you, specifically, in magecraft, no one calls magic rings horcruxes.

If you want to be "specific" like you said, then you shouldn't either. They're not the same thing. If you're saying "horcrux family" you're referring to the taxonomic grouping of Phylacteria, which includes things from soul gems to philosopher stones to sympathetic portraits. So your reasoning for calling a Ring of Power a horcrux is because random people "call the immortality macguffins horcruxes?" Let's get soul jars and boxed hearts in there, then, too. Also, calling someone a lich or an necromancer? It's not one or the other, that's not how taxonomy works. They're both. The One Ring is a magic ring and a member of the phylactery family. But that's not what you said. You said a jackdaw is a horcrux, which is not true unless you're okay with calling all members of the horcrux family horcruxes, which means you'd call philosopher stones, soul gems, and other soul jars horcruxes, too. Which you said you don't. It's okay to just admit you're wrong, you know?

There are a number of differences in both creation, nature and destruction that must be addressed if we wish to consider this question fully.

The first thing to be considered is that a Horcrux is a device designed to cheat Death. Such a device is of little use to a being such as Sauron who is claimed to be truly immortal (As he is of the order of Maiar as mentioned in the Valaquenta and Ainulindale). Indeed the One Ring of Sauron actually acts in a mode completely incompatible with what little knowledge of Horcruxes can be gained from the 'Harry Potter' historical documents.

As previously mentioned Sauron is already immortal, with a stated lifespan equal to the 'universe' of Arda. It is stated with the Silmarillion and other related documents that a Maia (singular of Maiar) is 'tied' to the world and cannot leave until the world is unmade at an unknown time in the future. Thus he obviously has little use for an item intended specifically to stave off a mortal death.

Further we can look at the operation of the items in question. Horcruxes are stated to have some level of rudimentary intelligence, such as in the case of Tom Riddle's diary Horcrux which is able to maintain a rational conversation over a number of months. The One Ring is not presented in such a light. It is presented as having no driving will of its own, instead it works to undo the will of its bearer and turn them towards the purpose of Sauron.

We can also look at the method of creation employed by both Sauron and Voldemort. Horcruxes are said to require a piece of cold-blooded murder to complete the act. There is no mention of such an act by Sauron within the historical texts. In addition it seems that the 'humanity' of Voldemort is said to be undermined in some fashion by his creation of Horcruxes. Sauron is in no way lessened by the creation of the Ring. In fact he gains power, it acts as a focus for his will and allows him to control other ring bearers at a distance (see, Nazgul).

We must consider the nature of the items in question. Voldemort is said to have placed a part of his 'soul' within his Horcruxes while Sauron merely placed much of his 'power' within the Ring. Indeed within the mythology laid out within the Legendarium the 'soul' as a concept is wholly immutable by lesser powers, only Eru (the primary god of the pantheon within the Legendarium) may toy with the 'Secret Fire' in such a fashion.

Finally we come to the results of their destruction. The destruction of the One Ring immediately causes Sauron to become greatly weakened (but not killed, as he still is incapable of death). He is weakened so extremely that he 'can never again gain corporeal form'. Voldemort, on the other hand, cannot even sense when his Horcruxes have been destroyed by others and apparently has no way of sensing when they are being used.

Thus I think all the evidence would suggest that Horcruxes and the device known as the One Ring are fundamentally different objects.

There is some widespread confusion in this matter as the answer is quite obvious. That answer is no.

Sauron didn't forge the ring to achieve immortality, he intended to use the ring to more easily influence the free people of Middle Earth. That's why he taught the elves (namely Celbrimbor) to make rings of power. He overlooked the rings intended for the Dwarven and Human lords and enchanted them with his magic so that the wearer would be corrupted by his influence.

One obvious difference is that destruction of the One Ring was enough to effectively kill Sauron; destroying all of Voldemort's horcruxes were insufficient to kill him. In the case of horcruxes, the master soul has to be independently killed. This is, I suppose, a symptom of a more fundamental difference: by creating the Ring, Sauron diminished his own power to the point that the ring had to exist for his survival. The creation of a horcrux, on the other hand, removes an esoteric element from the creator but does not remove from them any portion of their power.