Typical jazz compositions are written expressly as vehicles for improvisation. Mainstream jazz tunes since the 1940s take the form head-solos-head. The head is a written melody, and the solos are improvised around the chord changes of the head. Scores for these kinds of tunes take the form of lead sheets, like the ones found in the Real Books. The lead sheet writes out the head’s melody and chord progression. The specifics of accompaniment, interpretation and tempo are up to the performers.
Sometimes lead sheets specify intros and endings, but very often they don’t, and it’s up to the performers to come up with them. A few third-party intros and endings are so memorable that they become de facto parts of the original composition. For example, Dizzy Gillespie wrote such a brilliant intro and ending for Thelonious Monk’s “Round Midnight” that Monk himself used them in all of his own subsequent performances of the tune.
Big band jazz will add quite a bit of additional composition to the head-solos-head structure. There will be written parts accompanying the solos, countermelodies to the head, more elaborate intros and endings, and composed sections between solos called shout choruses. Improvisation can form the basis for a lot of these passages — horn players will improvise a background part onstage, and then if it works it’ll get written down and added to the “official” score. Duke Ellington and Benny Goodman frequently worked improvised ideas by their sidemen into their compositions (some would say they stole those ideas, since the sideman rarely got co-composer credit.)
Like Mark Catoe says, there are some through-composed jazz works. My favorite is Monk’s “Crepuscule With Nellie.”
But even within such a highly structured piece, Monk varied the delivery quite a bit from one performance to the next, especially rhythmically.
There’s been a pretty smooth continuum between through-composed, classical-sounding music and completely off-the-cuff improvisation through the history of jazz, sometimes within a single performer’s work. John Coltrane started his career playing conventional head-solos-head tunes with written intros and endings, and ended it playing completely unstructured free jazz. There was a fascinating middle period where he was playing head-solos-head music but not writing anything down, just giving verbal instructions to the band. That’s actually my favorite music of his — the long, one-chord modal tunes from the early to mid sixties. Miles Davis also ran the gamut from tightly structured big-band jazz to chaotic freeform funk, and everything in between.