Yes, SSH is used as a mechanism for authentication, and it still requires some further specialized server due to some protocols you don't know about. The server is git-upload-pack or git-receive-pack, depending on whether you're pulling or pushing. Your inference that a Linux distribution could conceivably put these in a separate package does seem reasonable, since for example git-gui is a separate package in Debian. I don't know of any distros that do in fact package Git that way, but they certainly could.