Improvisation encompasses all these things...it is a very broad term. You can noodle, you can compose, you can embellish...it doesn't have to be on something that exists...etc.
Also I may have miscommunicated. All of this process I Described happens during a single session---I don't "bring a theme back later" like, hours later, I mean MINUTES later WHILE I am improvising. It is all truly spontaneous. Every aspect of the music is created originally on the spot, except my ability to play scales and a vocabulary of chords. That is to say, I have a physical vocabulary of techniques which can all be chopped up harmonically, melodically and rhythmically on the fly.
you said:
"Now...once you have composed some kindof melody," <<<this is what I do on the fly. I ALSO add/subtract to these melodies AS WELL as come up with them on the spot. I don't work them out. It takes a lot of practice to get to that point but it is well worth it, because it feels effortless even though everything you play represents the sum total of effort you put into your playing over a long period of time.
I'm not saying you are wrong---I am saying there is more than one way to look at it---there's nothing wrong at all with working out a melody and THEN embellishing upon it, but, as I am describing here it is also quite possible to improvise every aspect of your music spontaneously.
Let me describe it another way: Here's the typical split-up most people think of:
composer->performer->listener
I assume you believe improvisation should only be in the "performer" part?
I'm simply encouraging you to sort of muddy the waters a bit------there's no cosmic law that says that one person can't be the composer, performer, AND listener all at once. They needn't be separate.
One more comment---there is no such thing as wrong in music. That's just my opinion though.