Music means so many different things to so many different people and takes so many different forms that it's almost impossible to define...
The'music is a language' idea is common and since we use words like 'phrasing' and 'voicing' it's no surprise that it gets used.
But a language is a means of communication and words and phrases have a definite meaning that is commonly accepted. Music doesn't have that, there's no dictionary or phrasebook and musicians can rarely explain what it is that they're trying to say. Music textbooks and teachers rarely concern themselves with telling anyone how to go about expressing their thoughts and feelings..
What does a minor7 chord actually mean and why would you want to use it?
So what are you trying to communicate with this 'language' of yours? Does it have to be a story, or can it be a poem, haiku, learned discourse, dream world, emotional state, stream of consciousness or just an informal chat? You can shout, whisper, murmur, moan, laugh, cry, exclaim, scream, growl, grunt, sigh, mutter, giggle and groan with your voice, but can you do that with your saxophone?
Improvisation is just one means of expressing yourself - for some people a kind of instant composition where you create something new each time - and in some form or another improvisation occurs in many kinds of music, not just jazz.
But if improvisation gets mentioned, it's almost always discussed in terms of jazz and in particular the kind of jazz that evolved in the 40's and 50's. Jazz textbooks seem overly concerned with what notes to play over the chords, but if you follow a rigid method there is the danger that you'll end up playing in the same way on every tune.
Of course there are many wonderful improvisations where the tune is hardly relevant, just a starting point for something greater. You can go wherever you want, it's your music.
"We are all different and we all have different ways of saying the same things. Find your own nature and see what you want to do with it" - Steve Lacy