"He plays guitar" is an informal variant of "He plays the guitar."
Usage varies according to the instrument and the kind of music that is played. With instruments like the guitar, the piano, the drums, and the saxophone--instruments used in jazz and popular music--the article is often omitted.
With instruments associated mainly with baroque or classical music, e.g. the flute, the oboe, the French horn, the harpsichord, the bassoon, the definite article is often used.
Because the piano and the guitar, as well as other instruments like the bass (viol) are used in playing all kinds of music, the definite article is more likely to be used when talking about a classical musician's type of instrument.
The distinction, however, is far from clear-cut. You see and hear both versions, often according to the level of style--whether formal or informal.
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