Both forms express an obligation not to do something (although one phrases it by declaring that permission is missing).
I figure that must not sounds a little more urging but what I am interested in is this:
Are both phrases semantically interchangeable or are there situations in which only one will work? If so, why?
Best Answer
The phrases do not mean the same thing, and while they may often be used interchangeably, this is not always the case.
For adults, this is an admonition based on objective reality. It really means
But in many situations, there is no authority that controls this activity. If we are talking about your machine in your home, it really doesn't make sense to say
Not allowed by whom?
For children, we often impose an authoritarian limitation because they don't yet understand the practical limitation, and so the terms are often substituted. Also, for adults, practical and authority restrictions often coincide.
Sometimes must not is used to indicate lack of permission by an authority, even where there is no real practical risk
In short, for the vast majority of circumstance where not allowed to works, must not will also work. For some circumstances where must not works (where there is no rule, but real practical downsides), not allowed to does not.