"The brothers were fighting over/for a slice of pizza."
I've seen people use both for expressing pretty much the same thing. But here's something I need to know. When I say 'someone's fighting for a slice of pizza,' it sounds to me like they are fighting to decide who gets to eat it.
But when I say 'someone's fighting over a slice off pizza,' it sounds to me like it can be either to decide who gets to eat it or it could be that one of the brothers ate it and the now they are fighting because the other brother wanted to eat it too.
Could anyone please help me understand the difference?