Breaking and cutting yarn is basically the same thing. There are various reasons for which you might be instructed to break the yarn, for instance when you do a pullover in more than 1 piece, you have to break the yarn after each finished piece and later join everything together.
Breaking might be called like that, because you can "break" the yarn by pulling hard on it. Cutting might be cleaner. To everyone his preference. Basically it's the same thing.