Designated Magnum primers can be used in any cartridge, with any powder type, if the load is worked up from a data manual starting powder charge.
That being said, the main reason for using magnum primers, and the main reason that they are designed with a hotter flame front, is for use with spherical (ball) type powders which are usually more difficult to ignite properly.
They may also provide better ignition of powders of all types, when using large capacity cases that hold more than 70gr.
In most situations, they do increase pressures with identical powder charges compared to standard primers.
Here is a short summary of the A-Square test of primers in the Remington 7mm Mag. as published in "Handloader" magazine.
160 grain Sierra boat-tail, 66.0 grains of Hodgdon H-4831 and Winchester cases.
Winchester WLRM (magnum) 3045 fps, 67,600 psi
Winchester WLR (standard) 3024 fps, 64,400 psi
Federal 215 (magnum) 3036 fps, 61,400 psi
CCI 250 (magnum) 3039 fps, 61,500 psi
Remington 9½ M (magnum) 3041 fps, 59,300 psi
CCI 200 (standard) 3011 fps, 54,800 psi
Now that is quite a large spread.
NCsmitty