Reading down, I'm not sure if you changed your question - however, I'll answer as it is now.
I would take it to mean, club is a club (patrons dance/bar) and strip club is where strippers perform/bar.
So no - not the same thing.
I don't get it. Your significant other told you that they went to a club. Why is that hiding something if he told you?
Lax to me means you don't care ...
I'm not following.
ETA:
I read the bit you added. So your main concern is you feel your man is lying to you. Ok now I get it. You're ok with strip clubs because you trust your man there, but you don't trust your man in a club where women could hit on him. So essentially, you don't trust your man.
I would trust my hubby no matter where he went. He's gone to regular 'clubs' on conferences because that's where they've been held (they all went out to them afterwards) and I don't worry about it.
So has your guy given you cause to worry in the past, or is this your issue? Figure out why you are concerned, and go from there.
If you have red flags going off ... I would just deal with them. If he's lying .. not good. If it's your own insecurities, also not good. If he's lying, that's a relationship problem and ultimately you have to deal with it (figure out how you will react). If it's you (insecure and looking for reasons to doubt him) - maybe a session or two with a counselor.