An interesting article  explains the difference between play and game and therefore between playfulness and gamification.

He summarises his reasoning with some bullet points:

– Play is free form and has no extrinsically imposed goals. It is done for fun or joy.
– Games add defined goals and rules to play (such as challenges).
– Toys are objects that can be used in play or games.

Games and toys are a subset of play.

– You play.
– You play a game.
– You play with a toy.
– You play a game with a toy.

Full article here.