Hi,
Sciencelady was right on the money w/ the push-ups being a major core exercise so they definitely are different than bench presses or flyes.
There are variations you can do such as doing them on a stability ball, the more your torso is on the ball the easier they are, the further down your legs you go the tougher.
Also, a cool variation w/ a swiss ball is to actually place the ball against a wall and do standing push-ups w/ you hands on the ball. When you find just the right body position (leaning towards the ball) your whole core should start "talking to you!
".
Whenever I first show this to my clients they look at me like "what will that do for me", but when they find that "Sweet spot" their whole mid section starts to shake from trying to maintain stability. Plus the unstable surface of the ball really fires up a lot of other muscles in your arms and upper torso to help you stabilize while you are doing the pushup.
Oh, one way you could incorporate the core more if you absolutely don't want to do pushups is to do resistance tubing presses from a split stance position. So you'd anchor the tubing into a door (make sure it's a heavy duty door that can lock, like a typical front door or garage door), then place one foot in front of the other in a standing position, walk out until you feel suitable resistance and then do your presses or flyes.
This position engages your core as a stabilizer since you are in a standing position and don't have a bench to stabilize you.
You can vary it by pressing one arm at a time, either all one side then the other, or alternating.
You can also just hold the handle in one hand, place the other handle on the door knob (but make sure it is very secure (this works best with flexible handles and probably won't work w/ the molded plastic ones as well) and walk out until you feel the resistance.
Then from there do one arm presses at a time from a split stance position. If you're working the right arm, the left foot should be forward. This really engages the core.
A further variation is to add rotation, so as you press forward you rotate the back foot as you press, so this adds a dynamic core component to it (the other way works the core from a stability standpoint which is VERY important).
Hope this all made some sense
Best,
Scott