Phase 8: Manipulators; Chapter 1: Pawns and Knights

No it's not. Having your opponent in check doesn't necessarily mean you can get checkmate next turn, and you can put an opponent in checkmate without necessarily having had him in check at any prior turn (though on the SAME turn, any checkmate is also technically a check).

If you want simple, try this: "Check" means you've placed your opponent in danger which requires immediate attention. "Checkmate" means you've placed your opponent in certain doom.