I can only speak to my own use of the terminology but I consider Top/bottom to simply be a genderless way of getting around having to say Dom/Domme to distinguish the male from the female. It's just shorter to type Top/bottom. There might be a more complicated explanation to it, but that's how I've been using it anyway.

The difference between slave and sub... I think that can be a more complicated definition. I'll leave it to someone with more experience than me to answer that one.