They are different. "to enlarge" means to make something bigger/larger "to zoom in", means to get closer to something, so it looks bigger. The thing is still the same size, but the viewpoint is different. Also, "Could you zoom in the screen" is incorrect, you cannot zoom in *something*. You can say: "Could you enlarge the screen?" or "Could you zoom in?" I might reply "I will enlarge the screen" or "I will zoom in". Also "zoom in" is quite a computer-related expression, whereas "enlarge" is more general. For example "The wedding ring is too small, so the jeweller will enlarge it". "The canal is too small for large modern ships, so the Government will enlarge it". You cannot say "zoom in" in these examples! Or "The photographer zoomed in on the face of the woman". You cannot say he "enlarged" the face of the woman - the face stayed the same, just his view through the camera lens is changed.

Yes, the expressions differ. The phrasal verb "zoom in" is quite specific and temporal. Enlarging a photograph lies in a different context. I might want to enlarge a photograph to focus more clearly on a scene, but that could occur at any time.