Play by ear is a term that describes the ability of a person to play any song with improvisation either by ear, from fake sheets, lead sheets, or chord charts. A person capable of such improvisation is also regarded as a musician. Typical classical players may realize that they are unable to play by ear because improvisation is rarely taught in traditional, classical training, which is why most classical pianists find it difficult to play anything off their heads.
There is a difference between a player and a musician. A player is someone who needs instructions or materials in order to play. A perfect example is a typical traditional pianist who needs prearranged score sheets in order to play. It’s analogous to an MP3 player without any MP3 files loaded. The MP3 player cannot play, simply because it has nothing to play. A musician is a player and an improviser as well. He or she, possessed of an imaginative mind, is able to create tunes and play them in any style he or she prefers spontaneously.