discovered by Europeans

The answer is rather embedded in the question. The common denominator for why cultures widely separated in time and space appear to have common attributes owes far less to actual similarities and far more to the folktales and religions of non-European nations (or other-European nations, or old-enough-to-be-gone-from-living-memory peoples, etc.) being interpreted through the lens of contemporary Westerners, and especially a 19th and 20th-century effort to categorize, define, and schematize.

I touched upon this previously in Why are there so many types of undead and similar monsters in mythology that transmit their status by biting?, and the thing is that if you go back and look at various historical accounts of various beasts, monsters, spirits, and legendary entities and compare them to more contemporary versions of the same ideas - the results often don't match.

When you look at creatures like "vampires" for example, it is not true that every culture has some legend about a corpse that rises from the grave and sucks the blood of the living. Not even every European culture has that particular legend, or often has many folkloric variants, from evil wizards who send forth an astral form to vampire pumpkins and watermelons. There is no single definition of a werewolf, or how to turn into one or how to deal with one. Dragons vary from great worm-like beasts to wyverns to monstrous creatures of ill-defined-and-not-necessarily-reptilian aspect - and that's without leaving Europe.

Things that get called "vampires" or "dragons" by European folklorists and explorers in Asia, the Americas, Australia, etc. often bare only vague similarities to their supposed European counterparts. I touched on this in Why are dragons a part of so many different cultures?, but it bears repeating:

So part of the issue is that there are a number of different creatures from different cultures which have been subsumed under the general heading "dragon" (or equivalent term) when translated into a European language context - the Aztec Quetzacoatl, the Lambton Wyrm, heraldic wyvern, the Chinese long, the Babylonian sirrush, Smok Wawelski, etc. are all sort of crowded together under the term "dragon" in English, despite having very different physical appearances, habits, supernatural correspondences, etc. And in certain contexts, this has proven very useful - mainly I'm thinking of fantasy fiction and roleplaying games, both of which have benefitted from easy categorization. Even Tolkien in his Silmarillion used the broad term "dragon" to refer to fire-drakes and cold-drakes, winged and wingless; roleplaying games like Dungeons & Dragons and Shadowrun which take inspiration from Tolkien often have many widely varied creatures which are all collected under the label of "dragons" - and in part, the use of a common term tends to lead people to exaggerate commonly-perceived attributes (scaly/serpentine/reptilian natures, flying, wings, etc.), even as they dismiss things like "Does it have wings? How many legs does it have (if any)? Is it good or evil?"

So, part of the reason why there are vampires and dragons in so many different cultures is because people were happy to slap the label onto many different creatures - for many reasons. In other cases, many individual accounts are combined and contextualized into generalized narratives which may not be accurate. In Dave Goudsward's Sun, Sand, and Sea Serpents (2020), he traces many individual accounts of "sea serpents" - which often turn out to be anything but; the generic term "sea serpent" is often used for convenience, even if the accounts of encounters real, exaggerated, imagined, or received in translation from an indigenous source don't conjure up the typical image of a long, sinuous serpentine beasty of the sea.

Great answer by the esteemed /u/AncientHistory. A few thoughts to add to this.

Your question contains "common elements" that are expressed repeatedly on this subreddit - all without any clear historical or other connection! The question simply arises independently and frequently, so we must consider some other reason as to why it frequently appears!

My typical answer to your question is as follows:

There are several ways to address apparent similarities. The first is the simplest explanation, namely that while oral traditions may seem similar, that can be deceptive. The human mind is inclined to see patterns. Seeing animals in the clouds or faces in linoleum does not mean that there are actually these entities (or their spirits) in those locations. We arrange the world so it makes sense, and seeing patterns - and similarities - is one way to achieve that. So first, similar-seeming traditions are not necessarily that similar nor are they necessarily connected in some way.

The second way to explain similarities is to consider the possibility of diffusion. Traditional narratives diffuse, and although they change over time and space, some core motifs can (and do) survive the process. This can explain some similarities: in this case, similarities are part of a historical process that involves diffusion. Descent from a common ancestral body of traditions explains why "cousins" have similar oral traditions; diffusion from one culturally-unrelated people to another explains how some similar stories can appear in diverse places.

A third possibility is less difficult to deal with and has yielded some extravagant contemplation. This is, namely, the idea of the common human denominator. Some of this is easy: all people die and experience death, so it is not surprising that all folklore deals with death in some capacity. Because most people historically have preferred to contemplate the idea of survival of death, it is not surprising that most oral traditions deal with ghosts, walking dead, etc. While similarities may not be profound in all cases, the common human denominator causes some similar attributes.

The same can be said for many other aspects of the human experience: sex and death, but also the weather, flooding, animals, etc. All people share a great deal in their experiences, so it is not surprising that internationally, oral traditions would be similar.

Taking the idea of the common human denominator a step further, Carl Gustav Jung postulated the idea of a collective unconscious - the idea that there is a shared body of archetypes that is entwined in everyone's consciousness, part of a universal fabric that manifests in our narratives and in our dreams, etc. This idea was transformed for more popular consumption by Joseph Campbell, but regardless of the promoter of the idea, the foundation of this way of thinking is the same. This is next to impossible to evaluate. It is nearly a spiritual explanation and it must be taken on faith - or not - depending on the person.