Do they have to?
The differences between these words is pretty simple and straightforward. It is important to use the correct word, as precision of meaning matters.
Even though "shall" is the currently preferred word in the Model Constitution due to historical realities, legal language has moved away from its use and toward the more modern "must".
Note: See #3 on Drafting Legal Documents on Archives.gov for more details.
Note: For a more full discussion on "shall", see this FAA article.