‘Classical unicorns’ are the original look all unicorns once had, but after thousands of years of interbreeding with pegasi and earth ponies (who had their own original looks) unicorns started to look different, losing the cloven hooves, curved horns, leonine tails, and extra fluff. Classical unicorns still exist, but they are very rare now as they are the result of only purebred unicorns, and a vast majority of them are stuck-up about other unicorns and ponies and have a superiority complex about being special (n their eyes) and are rarely seen in modern society.
The few that are not afflicted by this snobish attitude are fine with mingling with other ponies and their unique appearances tend to make them looked upon as interesting and cool.
Classical unicorns as a whole have a slightly higher chance of having more powerful magic, however this has nothing to do with their appearance, it’s just chance, but it doesn’t stop them from pretending they are more powerful, they just so happen to be more educated on magic.
The imperial unicorns from Mistmane’s backstory are a mid-stage of unicorns from classical style to modern style.