Does a recommendation have to be from a professor from your university?
I am applying to an applied math graduate program in the US. I frequently interact with professors from other institutions. Some are from math departments and others are from other departments. Could they write letters of recommendation for me?
Yes, they could write letters for you. In fact, strong letters from faculty outside your home department or university will likely help your application.
One caveat, though: A strong recommendation letter must praise your potential for research in applied mathematics, not just in the writer's native discipline, in specific and credible detail. Moreover, it must be clear that the writer has the expertise to judge that potential; that expertise may not be clear from their departmental affiliation alone. So you should consider asking your references to include a short paragraph in their letter, explaining their own applied math background (either as a researcher themselves or as a reference for past successful grad students).