I do understand this, but often these are just terms to use in critique. They are not the way others use these terms. However, milieu, by definition, in any place other than a very small post-left minority is synonymous with a movement. In fact, where both these terms are most used are in art (ie critical) theory where they mean specific moments in time.
As for movement building, there's a grey area. People want to pitch movements as an "activist" thing, and even then, the word "activist" has to be appropriated to mean something other than what the rest of the world defines it. Movements are definable, like milieus. There was a genuine "give up activism" movement and "give up movements" movement, just like there are stringent "anti-political" ideologies. People worked very, very hard to to "build" those anti-movement movements and spread anti-ideology ideology. It all comes off as hypocritical, and that's why newer terms are used. Even so, the origins of these words and their relationship to the Left and why they are used in common parlance still stands.
To be fair, milieu is a francophone extraction, which is literally, "the structures or scenes that produce the art movements." Movements are the "intellectual tendencies or scenes." Intellectual tendencies are the structures (or scenes).