We have lots of words for moving. Run, walk, jog (a newish one adapted from somewhere else), skip, trot, canter, sprint etc.
All these mean different things. And are not interchangable. Was Linford Christie a sprinter or a jogger?
Likewise we have lots of words for making things. Make, create, manufacture, produce, build, model etc.
It is my belief that these words are not 'truly' interchangable. Manufacturing, for example, was adopted and popularised in the 1800's to describe what happened in factories. They adopted this word (which derives directly from "makes from metal") because other words did not describe the new processes properly. When this was done 'manufacturing' was a good thing, because it was going to revolutionise our lives, but now it is a bad thing that is destroying the planet and so 'nicer' words are being associated with it.
However, the dictionary does give the word 'manufacture' several meanings, one of which is to "concoct or invent, fabricate: manufacture an excuse", but that is a more colloquial or poetic use of the word.
I am just for purity of language, not from any fascitic view point, but purely from a plain speech point of view. When words are used 'poetically' then surely they are being used for the purpose of mis-information and to make things look rosier than they are.
Our discussion here is about an essentially trivial thing but the principles go a lot further.
I do concede a certain amount of creativity (using your definition) in most jobs, as you say it is a fundamental part of being human.