"strip club" and "nude strip club" what difference?

That's basically it. You've got three basic types of clubs: bikini go-go bars, topless, and full nude clubs. So it's nothing comes off or it's all peek-a-boo style flashing for bikini, the top comes off but not bottoms for topless, or tops and bottoms can come off for full nude.

I see four types of the clubs on the website.Its as you said bikini go-go bars, topless strip club, and full nude clubs.I see one more - just "strip club". But then what's the difference between "topless strip club" and "strip club" or "nude strip club" and "strip club" ???

I would say if it doesnt state full nude, its probably not full nude. But ymmv. Every club is different. Best to read reviews

It's all for the locals who live in areas where there are laws regarding the sale of alcohol and dancing. Generally, in those areas Nude Strip Club means no alcohol is served because the dancer may get totally nude on stage, Topless Strip Club means the dancer can take her top off and Strip Club means the dancer can take her top off but must wear pasties.

Vagina

There are the occasional areas (like Miami FL and Portland OR) where the club norm is both full nude and full alcohol (like a full liquor bar, not BYOB). My guess is that the “strip club” category is for exceptions like that. Or possibly it’s a category clubs that are full nude, but not on stage. And there are indeed pasties, which can be full on fabric paint or clear nail polish over just the nipple (weirdest “pasties” I know of).