It's been retconned since S2/S3 sometime, the pilot still says "The older sister used her unicorn magic to raise the sun...", but after that, they're definitely different things.
Probably as a way to expand the lore, now that pegasi have distinct pegasus magic, and earth ponies have distinct earth magic, it makes sense to make alicorn magic a separate type as well.
Take for example Zecora's line from Princess Twilight Sparkle 1 "...It only responds to Alicorn magic..." during the cum-potion scene. The spell Twilight uses doesn't even look the same as her regular unicorn magic.
Or consider Tirek and the numerous references to alicorn magic in Twilight's Kingdom: Tirek specifically wants alicorn magic, even if he has all the other magic in Equestria, he needs alicorn magic for some reason, and alicorn magic specifically.
As an added bonus, it was no accident that Fluttershy tells Discord something among the lines of "What if you had a friend to discuss Chaos-based magic with".