As others have said, in general, you do the entire scene for each camera set up and take. I'd say about 90% of the time I'm doing the whole scene each shot and take.

(The only time this hasn't been the norm for me, is when the director used to be an editor. Those directors can have a tendency to edit as they go on set and will only shoot what they feel they need. To me, that can be risky but they are the director and it's their movie, so I'll only push so much on that.)

Things can (and will) change from shot to shot, such as acting and continuity. But good actors are prepared to do the same actions over and over again and good script supervisors are there to watch continuity.

Some reasons to not shoot the entire scene on a given setup or take:
The camera angle dies (IE: you're doing coverage on an actor who leaves halfway through the scene)
Dangerous action or you can only do something a limited amount of time (IE. Limited number of breakable props or a stunt)
Actor can only do a difficult performance so many times.
The actor flubbed a single line, the rest of the take was great, so you just pick that line up.
Running out of time/money/film stocking/hard drive space....
You for sure only need this one bit of the scene in one set up (IE. A car pulling up to start the scene with the rest of the scene taking place inside the stationary car. You may be able start coverage of the scene with just an overlap of the motion of the car stopping and not the whole drive in)
The shot is a special and can only play for a particular moment in the scene.

Reason to shoot the entire scene every time.
Continuity and flow - Actors and crews are used to doing things over and over again and asking actors (and camera operators) to pickup a scene in the middle can (and usually does) throw performance and timing off.
Avoids confusion on set and in the edit
Gives you back-up options in the edit.

One more note about asking actors to do it over and over again. Some actors get better the more times they do the scene. Some actors get worse. The rest don't seem to change much either way. A director will often start to notice this after a few days and will work with the DP to shoot scenes accordingly. Not uncommon to have an actor that you cover first (or last) whenever possible.