You'll notice right away that there are a few very obvious differences between Scrabble and Words with Friends that can affect your game. (And they are obvious for a reason, as we'll see.)
The board is set up completely differently, for one. There are more triple-letter spaces and fewer double-word squares. The Scrabble board's bonus squares are laid out in a lovely X in the middle pattern; Words with Friend's chooses a subdued diamond pattern. That means you're working less toward the corners in Words with Friends.
Another big difference is that there are 104 Words with Friends tiles versus Scrabble's 100, which means a different distribution of tiles in general. (For the record, Words with Friends has one more D, one more E, two more Hs, one less I, one less N, one more S and one more T.) Twelve of those letters also have different point values. So be careful not to get too attached to the Words with Friends tiles if you're entering a stiff Scrabble competition; you might be torpedoed by your Words with Friends assumptions.
Now why those differences? Copyright, almost surely. If Words with Friends has a different board, different standards of play and different piece distribution, it can legally claim it's a different game from Scrabble. And you, in turn, can keep tapping away on your phone to your heart's desire.