...I just find it quite deceiving to know that the music style that is all about improvisation isn't improvised at all.
What is your personal definition of improvised? The reason I ask, is that as I work through the process of learning music in general and jazz in particular, I've found that my definition of what happens in jazz has shifted from "improvised", which basically means "made up on the spot" to "communicated" which I take to mean, "expressing a sentiment using an established framework".
Using the English language as an example, we communicate using 26 letters, arranged in agreed upon patterns called words. We use words in an established framework to make sentences which expresses some kind of sentiment. How you choose to arrange the letters and words can make you sound like Winston Churchill... Or Larry the Cable Guy...
In Western music we use 12 notes, which you can arrange into patterns. then you can arrange these patterns in various ways to create musical sentences, or phrases. How you choose to arrange these notes, patterns and phrases can make you sound like Chick Corea or John Coltrane. Or someone else...
But the take away from all that, is that it's not made up. To me, "improvisation" operates within a framework, but of course, music being what it is, it's simply not as tightly defined as using words and sentences. But the point is to communicate.
I saw this video which was billed as "the worlds worse music" A computer program was created to generate music that has absolutely no pattern associated with it. Since the human brain is pattern oriented, the music naturally was horrible. There was nothing to connect to. When I listen to Coltrane, I can here certain phrases that he uses a lot. Like in nearly every song he plays. It's like when we use sentences with a lot of "and" and "the" or "of", etc. There are things we just say a lot in almost all of our personal communication. Those are the "licks" of language. We don't make up words when we talk, so improvised solos, to me, is no different.
So ultimately, you are correct. It's not improvised in that it's not made up, in the strict sense of the word. But it does happen instantaneously which gives the impression of being made up.