My (ETA:
old) school:
1. Heated argument -- nothing, someone might be sent out of the class or they'd both be told to go away to cool off
2. Pushing -- they'd be scolded, pretty much the same thing as a heated argument
3. Brief fight and the teacher hears about it afterwards -- they'd get a detention, or if the teacher is nice they'd talk to them and ask them about it, things like why it happened, but not do anything
4. Brief fight and the teacher breaks it up -- if they were lucky and the teacher isn't an ass they'd get a detention, and the teacher would basically deal with it him/herself. If they're unlucky the teacher will take it higher and there'll be a suspension. Suspensions were generally two days in my old school.
4. Violent fight and a teacher hears afterward -- definitely suspension
5. Violent fight and a teacher breaks it up -- likely suspension, POSSIBLY expulsion if the student consistently fights (or if they've almost killed the other kid lol)
***Time also matters. Is it exam time? Or what? I'm ashamed to say I got into a fight with a boy (though he came for me unprovoked, he was trying to make himself look good I think) and the fight got pretty messy; there was blood. Most of it was his (I'm not ashamed to say that my fists are like iron

) but because it was around exam time we both got detentions, rather than being suspended. Also if one of them is experiencing things, like a family member or friend has just died, then they may get let off.
OH! And the punishment is definitely dampened if they have a good record. Teachers will be more lenient if they know a student is good natured, because they will feel that the student must really have been pushed.