I was writing an answer and realized I don't know the difference. They're all flint striking steel right? What made one better than the one that came before it?
This is a good question, because from the linguistic and rational point of view, three of four mentioned devices could be described as 'flintlock' or 'snaplock' with the wheellock being the odd one out. This is because devices known in English snaplock, snapha(u)nce and flintlock operate on the same principle and incorporate a spring-loaded lever (hammer) with a piece flint attacked that after pressing the trigger moves forward and strikes (snaps) against a piece of steel producing sparks that ignite the priming charge and consequently cause the weapon to fire. But in practice, mentioned names are used to differentiate between specific models of the igniting device, each with its specific traits.
Snaplock is a name that is generally reserved to a simplest of the designs introduced around late 1520s, with the both hammer and the striking steel being spring-loaded and the flashpan being either left exposed or closed by a cover that had to be closed and opened manually. To fire a loaded weapon, one needed to cock the hammer, open the flash pan (and prime the gun if it was to be shot immediately after) and move the striking steel in place.
Snapha(u)nce or Dutch lock (from ger. Schnapphahn or 'pecking hen') was an improvement of snaplock introduced somewhere around late 1540s. It was characterized by the automatic flash pan cover that was opening automatically after the hammer has been released via the simple cam pushed by the falling hammer that engaged the pan cover, opening it a fraction of second before the contact between the flint and striker.
The flintlock proper, that began with the introduction of the Mediterranean lock (also known as Roman or Catalan/Miquelet lock, with the difference being chiefly the construction of the main spring and its interaction with the hammer) in mid 16th century account for the latest improvement and, for the most part it was also the simplest one. Its most discerning feature was the frizzen or the piece that acted both as the striking steel and a flash pan cover. As the safety sear allowing the hammer to 'half-cocked' (i.e. being pulled away from the pan and thus making priming easier but giving no possibility to release it by a press on the trigger) has been already commonplace, all the shooter need to do, was to prime and close the frizzen, cock the hammer and fire. The frizzen was mounted on a hinge and supported by the spring that was strong enough to keep the pan securely closed and provide enough resistance to produce sparks but at the same weak enough to give way after being struck by the flint. It has been later slightly modified, resulting in the English or French lock (also known as battery locks) designed in 1620s that were characterized by a different shape of the frizzen and its spring, but the principle of operation remained largely the same until phasing out of the flint-based ignition systems in favour of caplocks in 1820s.
As I said above, the wheellock, introduced most likely in very early 1500s in northeastern Italy (first depiction of the mechanism appears in Leonardo's works known as Codex Atlanticus dated 1493) is an odd one out. It is, theoretically, still a variant of the flintlock, as it uses a flint to generate sparks (although a pyrite was another a popular choice), but its method of operation is different. In a way, it is an exact opposite of the snaplock, with the hammer holding the flint remaining stationary during the firing and the sparks being produced by a spring-loaded serrated wheel (hence the name) that rapidly rotated and scratched against the flint. It can be argued that with the longer action, the stream of sparks had a longer duration thus increasing chances of the priming charge catching fire, but the mechanism was soon abandoned due to its serious drawbacks. The spring was strong and short, requiring a large force to wind it, what resulted in the necessity to use the special key (not unlike a modern ring spanner) that was too large to be a fixed part of the gun and as a separate element it was always one item more to take care of. Furthermore, the lock was quite complex, as with only flat springs of adequate strength being available, the mechanism required either precisely modeled cams or miniature chain links to properly turn the tension force into rotary movement. This, although not a real problem in hunting weapons, was an obstacle in mass-produced, heavy-duty military firearms and a reason why the wheellock coexisted with much cheaper matchlock firearms and flintlock and has ultimately been replaced by simpler and more reliable variants of the latter.
An important note, and something that I wish a lot of books and web pages trying to explain these categories would make clearer, is that this is really more one of those victorian/edwardian-era collector classifications rather than one that anyone at the time actually understood. Generally "snaphance" was the most commonly used term through most of the 16th-17th century for any mechanism that wasn't either a matchlock or wheellock, which included everything from actual snaphances to doglocks, miquelets, and even "true" flintlocks since they all basically follow the same design principle of flint strikes steel and makes sparks. The actual snaphance with a separate striking plate and pan cover may not even have been all that common and generally seems to have disappeared pretty quickly after the first decade of the 1600s. Conversely "dog locks" and some other older style locks occasionally continue showing up even well into the 18th century so "flintlocks" weren't always true flintlocks either.
With that out of the way, the main distinguishing feature tends to be their safety mechanism. With the snaphance there didn't really need to be one. Since the striking plate and pan cover are separate, most of the time when not ready to fire you could just swing the plate up and out of the way, meaning that if you accidentally pulled the trigger when you didn't want to, the flint would just slam forward into nothing, and so nothing would happen. Alternatively having the striking plate pushed back out of the way might use a mechanism to prevent the trigger from being pulled in the first place or do other stuff like keeping the pan from opening when you didn't want it to. Ideally, especially if you were planning to use the gun from horseback, you'd also want it to include some spring or mechanism which causes the priming pan cover to open on its own at the same time you shoot so that you don't have to worry about manually opening the cover beforehand and then accidentally having the priming powder blow away or get shaken out before you actually pull the trigger.
With later designs, the frizzen that the flint strikes to make sparks and the pan cover were usually combined into a single L-shaped piece of metal, which made things simpler and meant fewer moving parts, but also meant that you couldn't just leave it up out of the way when not ready to fire without all your priming powder falling out so there were other methods developed to keep the flint locked in the cocked position. The "English lock" and similar locks that weren't english would use a slot and a sideways moving bolt or sear to secure the hammer in place at either the half-cocked or fully cocked position. It could then be released before firing either by pushing it out of the way or by pressing a button or lever somewhere which would then leave the hammer ready to fall as soon as you pulled the trigger. The "dog lock", which seems to have become one of the most popular designs in the 17th century just used an external hook or "dog" which could be swung forward to latch onto the hammer and keep it in place, and then released when you were ready to pull the trigger. Then there are "Miquelet" lock and similar designs would have a bolt or sear that automatically slid into place and and kept the hammer from firing when pulled back into the half-cocked position, but would then release on its own as the cock was pulled all the way back into the the fully-cocked position. Essentially a gun like this would be more or less identical to a "true" flintlock to operate, the only difference being the internal mechanism. Lastly, what is considered the true flintlock ended up using just an internal tumbler with multiple notches, one of which would lock the hammer in the half-cocked position and prevent it from being fired, while the other locked the hammer into the full-cocked position and did allow the gun to be fired. Overall this seems to have eventually won out as the most straightforward to operate with the least moving parts. But despite first showing up with the others sometime in the early 17th century, it still took quite a while to catch on as universal.
There are a lot of other different classifications that are sometimes used to describe weapons that mix and match multiple designs, use slightly different parts, change where the spring is and whether it's pushing or pulling from the top or the bottom. But again we're talking about a period where there wasn't really any standardization and gunsmiths would often just experiment with whatever and it's mostly just going to depend on his skill and experience how good the gun is. A well-made and well-designed snaphance probably would work much better and be much more reliable than a poorly-designed flintlock and vise versa.
Especially if you're say, a smith in jamestown being asked to convert old matchlocks into firelocks, you're mostly just concerned about cobbling bits together into something that works.