At least in the UK/London, #1 would be considered a "bar" (distinct from a "pub"), but as far as my experience goes (probably not been on a proper night out in London in 5+ years now) paying for a table is pretty much unheard of, unless it is a deposit/minimum-drink-spend for a pre-reserved table that then comes out of the bill at the end. To me paying for a table just seems like a ripoff.

#2 is as described, apart from there is probably entirely mainstream and not particularly LGBTQ (although there are dedicated places that specialise in that sort of thing)

Both #1 and #2 are usually over-priced and mostly filled with tourists or hen/stagg parties, and as such "uncool".