alot of the same muscles are used, mainly chest, shoulders triceps. But the exercises are very different. On the bench press, you pin your shoulderblades back, to be stable, they are NOT free to move, in a pushup they are free to move. In a pushup you move your body away from the floor, in a bench press you move the bar away from the floor and from you. Also, in a pushup, the further up you go, the more decline the motion gets, since your feet are on the floor.
You also have a different stability requirement since your body has to be held like a plank, so stability is simular to the plank exercise. Some people cant do alot of pushups because theire core stability isent good
With the scapulae free to move, more muscles for scapulae stability are activated, spechally if you do pushups the way they "should" be done, with protracting the scapulae at the top, getting complete range of motion (this is something you do NOT do on a bench press) this activates the serratus anterior more.
Testosterone Nation - Push-Ups, Face Pulls, and Shrugs
thats a good article about shoulder stability
theres a part where he talks about pushups that might be worth reading (actually, the entire article is def worth reading)
Hope that helps.