I believe you are referring to the .22's. Hyper velocity is .22lr loaded with a slightly lighter bullet (35-37 vs 40 gr?). The classic example is the CCI Stinger. Can be fired safely through most guns chambered for .22 lr.
The magnum is the .22 WMR (Winichester Magnum Rimfire). Different cartridge. Longer and SLIGHTLY fatter. Cannot be chambered in a .22 lr chamber.
Magnum simply refers to a larger cartridge case, as a magnum of champagne is a bottle twice the standard size.
Had the same naming tradition been followed, the RUM cartridges should have been called Jeroboams, and the big Weatherbees perhaps Rehoboams.
Hypervelocity should refer to velocities in excess of mach 4, or roughly 4,000 fps.
However both 'magnum' and 'hypervelocity' are marketing terms, so they really only mean what the marketing team decides they mean.
So to answer the question, "What's the difference?" the answer is "Lots." or maybe "Nothing", or something in between.