normal pushups? do you mean with elbows flared out? this recruits the chest(pecs) more than when the elbows track to the sides which focuses on the triceps. beam pushups are very similar to the elbow in pushups except hand placement is close. I think the close grip hits the pecs harder than a shoulder width grip.
pullups and chin work pretty much the same thing except undergrip pullups "chin-ups" get a bit more recruitment from the bicep because of the way the hands are turned in from the grip in the hang. the bicep is engaged more from the beginning in an undergrip than in an overgrip.
- pulls such as these work the lats and teres besides rhomboids, including the biceps and triceps and the erector spinae. during a pullup, your torso muscles are also engaged "abs".
handstand hold? trunk muscles, shoulder, triceps and biceps, forearms, traps and lats.
handstand pushup? same as above concentrating on triceps and shoulders