A magnum primer will have a longer and wider flame than a standard primer. The difference is usually only seen in powders that are very slow burning for the cartridge, also they can give better ignition with ball powders.

The difference in ignition can be large. Federal 215 Large Rifle Magnum are the only primer that give the best accuracy in my 300 Weatherby. The 454 Casull needs a Small Pistol Magnum(Small Rifle) primer.
I have had pressure decreases and lower rates of fire in a 9mm sub gun when using Small Rifle Primers. The primer was pushing the bullet free of the case and the powder was burning when the bullet was in the chamber throat. I happened in milliseconds but was very close to and obstructed bore.

There is no secret about primers, the manufacturers have all the data out and available on primers.