If you connect to Facebook account to play on playscrabble.com then you won't be able to play using the same Scrabble Go account on your mobile/tablet. The game doesn't allow for the 2 accounts to be used at the same time. You only need to fully close the app or browser and you will be able to continue with your game.
 
Playscrabble.com Message:
 
Mobile/Tablet Message: