Future continuous is used only when you have a specific time expression. Basically all the continuous forms are used only when you have specific time expressions. If you don't have one, then you can't use a continuous structure.
I will be moving to Beijing when you start your new job
I will be moving to Beijing tomorrow morning
Of course, you don't really need to say the time expression if it's implied into the conversation.
Do you have plans for next Saturday? Yeah, I will be moving to Beijing.
Be careful. Don't forget that the appropriate usage of will as an auxiliary verb in future tenses are these:
promises: I will love you forever
speculations: I think Artificial Intelligence will rule the world
immediate decisions: Are you ready to order? Yes! I will start with the chicken soup, please.
If you're talking about plans, use going to: I'm going to move to Beijing.
However, in colloquial English, those rules are not followed at all. =)
"I will move to Beijing this month" = you will finish and complete the action of moving to Beijing by the end of this current month.
This used to be called the future simple finished/completed tense, before 1989 when it was decided to make the simple language of English extremely completed to second Language English Learners: by renaming the tenses into complicated confusing names that even teachers get confused over.
"I will be moving to Beijing this month' = you will start/begin or continue the action process of moving to Beijing this current month, but you have not specified when the move/moving to Beijing will be complete; it is left open or incomplete/unfinished.
This used to be called the past or future unfinished/incomplete tense; before 1989; when it was decided to make the simple language of English extremely complicated to second language English learners: by renaming the tense with confusing names: that even teachers get confused over.
I hope this helps.
In daily speaking they are almost entirely used interchangeably to mean the same thing. Establishing if the move will be completed or unfinished is usually only discovered by asking a further question to the speaker, or waiting for the speaker to elaborate.
For all intents and purposes they mean exactly the same thing, but the difference is this:
"I will be moving" means that you will be in the state of moving this month. In short: the state of the action being performed will happen during that month.
"I will move" means that the entire action will occur during this month. So you're talking about the entire action as a whole, not the state of being in that action.
And if that was confusing, you can completely ignore it because it's such a tiny detail it doesn't really matter :)