How do you push up? On the left, the anterior deltoids are doing way too much work. The push up is a chest exercise and on top of putting your shoulders in a compromising position you are also effectively dis-engaging your pectoral muscles because your delts are handling the brunt of the force. .
On the right the shoulders are pulled down forcing your chest to pick up "the slack" from the shoulders which are no longer doing all the work. This also works stabilizers in and around your chest, shoulders, and core giving you a far more effective exercise than on the left.