The process and technique varies widely, assuming the drums are cut live at all (you'd be surprised how many bands with a drummer program some/all of the drums for their albums.)
Often, it's a question of what's most comfortable for the players, and efficient for the session, but it's extremely rare that a track is cut live by the full band anymore, I think my last sessions like that were in the '90s.
If a band has a persnickity guitarist for example, it's probably not best for them to try and record with other players who can quickly get a great take, as long as they don't have to keep stopping and starting. Such players should agonize about their parts later, without forcing the other guys to keep repeating the process just to get a good take on his behalf.
But if a band is on a budget, and won't have a lot of time in the studio, then they need to rehearse diligently, and maybe try recording as a band. It can certainly be done, but in this age of perfection supplied by producers and in turn demanded by the listeners, it's risky, and tends to encourage settling on everyone's part.
Drums first? I do that all the time, no problem, as long as I'm comfortable with the parts. I always write out the arrangement and specific parts as a roadmap.
Drums last? I've done a bunch of those as well. As long as the track itself doesn't have any egregious hiccups, the drums will fit right in. You'd never know.
Bermuda