Pwede and kaya

I was taught that "Pwde" or "Puwede" mean "can."

If I want to say "I can dance." It is "Pwde ako sumayaw."

Also, I believe that I can also add "kaya." I can dance = Kaya kong sumayaw.

First, what is the different between the two examples?

Second, "The maka- or makapag- affix indicates that the actor has the ability to do the action."

So what is makasayaw?