The "-i" option actually means "simulate Initial login" -- the idea being -i will drop you into a shell as if you'd logged in as the user in a fresh session. -s will also give you an interactive shell, but doesn't mess with the environment.

(And both -i and -s can also not give you an interactive shell, if you give it a command to run. The point is that it will run the command in the shell rather than just fork()ing and exec()ing like a bare sudo invocation would do.)