The final difference between the slice serve and the flat serve is the follow through. Because you were swinging in a different direction prior to and at contact, your arm is going to move in a different direction when you follow through.
We’ve split screened by flat serve (to the right) and my slice serve (to my left). I’m hitting to the ad court. Starting at contact, if we play this clip a few frames forward and then freeze it into my follow through, you’ll notice my arm and the tennis racket are pointing in different directions. On the flat serve my arm and racket are essentially pointing toward the ad court. On the slice serve, however, my arm looks like it is facing more toward the deuce court – again, because I had swung in a direct direction leading up to contact.
From a different perspective – this from behind – from contact it is clear that I follow through differently on my slice serve. My arm and the tennis racket are more to my left (because I’m left handed) on my slice serve than they are on my flat serve.
If I were serving at the camera, if I hit a flat serve my arm and tennis racket would follow through toward the camera. However, if I hit a slice serve my arm would follow through more to the side, creating some space in between my arm and the side of my body.