The fundamental rhythmic unit in jazz is the quarter note. Superimposed on this basic beat are melodies. Often melody lines consist of eighth notes, which last half as long on average as a quarter note. But no one plays music exactly as it is written, just as no two people would read a passage from a book the same way. If you want to hear music played exactly as written there are thousands of Midi files on the Net which are direct translations of sheet music.
Real musicians shorten one note, lengthen another, delay a third and accent notes.
It is all part of creating an individual style. Faced with a row of eighth notes on a sheet of music a straight musician plays a series of more or less equal notes. A jazz musician plays the eighth notes alternately long and short. The long note coincides with the basic beat, the note clipped short is off the beat. There is a similar but less pronounced tendency to play notes long and short in folk and baroque music as well as in popular music.