[upon_drumhead]

In Magic parlance, you play the game with a deck, but all your cards that you can build decks out of is called your library.

[kaoD]

This is wrong.

Deck is the set of cards that you bring to a match.

Library is a region of the game state: the cards that are yet-to-be-drawn. This only exists as part of the gameplay. Other gamestate regions are the battlefield, the graveyard...

[rtkwe]

Strictly speaking doesn't have to be undrawn cards given the myriad of ways you can put cards from other zones into your library, those cards may or may not have been Drawn from the library as well.

[t-writescode]

the library is your collection of cards from which you can draw and from which you do draw every turn.

It's not your entire compendium in and out of game, it's simply the deck of cards from which you (usually) draw and is distinct from your hand, graveyard and banished cards.