Game and play

   Play is both a larger and smaller term than game depending on how it's stated for example, on one side Play is a bigger term that includes Game as a subset. However in reverse its true as well: Game is the bigger term and shares Play within it. (Still these relationships are separate just linked by similar characteristics)

Games as a subset of play


   If you was to think of all activities we could call play, from a baby running with a ball to a young teenager rolling on a skateboard, to a community of online players, it seems that only some of these versions of play would actually be classed as a game. Playing Football is playing a game because there are formalized rules thats players must obey to compete and win.
   So going back to the baby running with a ball, this doesn't necessarily count as a game but it is a form of play because how to baby interacts with the ball. A young teenager skateboarding doesn't have rules so its not a game but is a form of play just depends how the teenager interacts with the skateboard. Although skateboarding can be a form of game from competing in competitions this way there is a formal set of rules added to the activity to make it a game.

Play is a subset of games


In another sense games can be thought of as containing play. The experience of play is but many ways of looking at and understanding games.
The play of the game represents one aspect of games, though play is a crucial area of games, basically you can interact and 'play' with a set of formalized rules this is why these to words have the same meaning vise versa.
  enjoyment and like are a big part of play I think. Enjoyment and like can make us want to play. So for example forget about football for the time beings; if you were to like the look of kicking a ball around a field this would draw you to play but not in a game sense, add formalized sets of rules to kicking that ball around the field then you would have a game and also enjoyment as a outcome because if you didn't have the liking of play then you wouldn't think of turning it into a game so with out some sort of satisfaction you wouldn't have something become a game.