A magnum primer is simply hotter, or at least is supposed to be*. The idea is that large amounts of powder -- and/or slower burning/harder to ignite powder -- needs a hotter spark to get it going. So large amounts of H110 (which for all intents and purposes looks to be the same thing as 296 and might even be coming out of the same spout) in a .44, for instance, usually want magnum primers. Powders like Unique, though, usually don't want or need a magnum primer even when used in magnum cartridges approaching magnum velocities.
The famous Elmer Keith .44 Magnum load with 2400 and a 250 grain LSWC was developed with standard primers, and is still a valid load today. Elmer was adamant that magnum caps not be used, as he claimed they increased pressure to dangerous levels. And usually, magnum primers do increase velocity and pressure. But Ross Seyfried noted, decades later, better velocity and lower pressure with H110 and magnum primers in the same cartridge. So as with most things internal ballistics, there aren't any absolutes. Most of the time you can get away with interchanging primers in the .44 Magnum, but sometimes you're asking for trouble. It really depends on the powder type and amount, the bullet style and weight, and even the amount of crimp you're using.
Clear as mud?
*There is some debate over whether all magnum primers are hotter than all standard primers. It may be the case that some company's magnum caps aren't as hot as other company's standard ones. Haven't tested it myself, so can't say for sure.
<edit> And seeing the powders you intend to use, in your shoes I would use the standard primers with the 2400 and buy some magnum caps for the 110/296.