(mapM_ print) produces a pure function that produces a single IO action, and (map print) produces a pure function that produces a list of IO actions. Neither has any effect unless called in a context that sequences the resultant actions into the main IO action that the runtime interprets (or a thread's action).
And my point is that the action that mapM_ ultimately produces is not actually executed unless you sequence it into the main action (or a thread's action). Since mapM_'s eventual action is a singleton, you can do this sequencing with any combinator taking a singleton action, for example (>>) or (>>=), but it must be sequenced nonetheless, the same as for the list of actions that (map print) produces, if you want those actions to be executed.