In terms of what they do - no real difference. In terms of how they do it - a bit different but basically the same user to user connection. The key difference is that unlike Napster, Winmx and all the current p2p programms don't use a central server which makes it harder for copyright owners to shut down.
Winmx is still running!! Although my cat is called Napster so is keeping the name alive!
Winmx is quicker now but if napster was still about it would probably developed in the same direction. It now takes bits of an MP3 from lots of different users instead of just the one so it's faster now.
There's every chance it will be closed down by lawsuits being taken out against the authors. Current thought seems to be that Kazzaa will be the next to go. Illegal to use? That's a hard one to answer and will probably depend on local laws. However most western countries have laws to protect copyright so distributing copyright material without permission is almost certainly against the law - making copies (of things you already own/licence) - possibly, though there's not much case law to back this.