I haven’t played Skyrim myself, but I expect it uses a system where there are different types of weapons, and each weapon type has its own set of animations. For example, your game might have axes, daggers, and swords. While you may have many different looking weapons in each category, there would only be one set of animations for each category.
That doesn’t mean that all the animations have to be identical for every weapon in one category though. Even though they may share the same key set, there are ways of making the animations different. For example, if you have a light fast sword and and larger heavier sword, you use the same swinging animation but play it slightly faster to for light sword since it would be easier to handle and swing.