Different Hair Styles

Hi,
I used to have long hair but now I just cut my hair to sllightly below armpit level, to experience short hair. I cut it in a U shape but now I am wondering if I should have cut it in layer. But I have no idea what the different styles mean. I would really appreciate it if someone could tell me what is the difference between layer cut, step cut, and U cut, and if there are pictures to be found online, please direct me to them so that I can understand clearly. And is it true that layer cut will not look nice on hair like mine, which though I call it short, is really quite long compared to the length of people who usually keep layered hair. And a few pictures of what I think are layered hair I have seen, they keep their hair in the front. I usually keep my hair at the back, so would layer be any good for that? Any help would really help me understand which style I want to keep my short hair in below I let it grow long again.

I'm not familiar with all the terms. I would suggest discussing this with your stylist or even experimenting with one of the simulation programs; numerous salons have them now.