Primers can often be interchanged - except when you're near the hot end of a particular load.
It's also important to understand that the term "magnum" when applied to primers does NOT have a set definition. Some makers' magnum primers burn "hotter," others longer, while others' flame extends farther out of the primer.
When loading with certain powders, a "magnum" primer is needed to ensure proper ignition. These are often thought of as "magnum" powders, and they need more spark to ignite. If the manual says to use a magnum primer with a given powder, use that magnum primer.
On the other hand, except for some "benchrest" primers, most mid-range, NOT hot loads won't show you much difference in velocity or pressure no matter what primer you use. Accuracy, on the other hand, may be all over the place...it kind of depends on, well, everything involved in that load.
So my take is to at least test your load if you change primers. Some people will say that doing an entire new work up for a different primer wastes components. But you won't know what, if any, effect changing primers may have unless you test it and see for yourself.