What exactly is the difference between orange and purple gear?

Orange gear is somewhat of a relic from when the Armor/Mod/Enhancement's couldn't be changed in Purple gear (which may still be the case for some items, sets).

Orange gear with all Purple mods should be equivalent to Purple gear with the same mods.

There is no real difference between orange rarity gear and purple rarity gear other than the item's rarity (which, as you've rightly pointed out, is a little dubious since you can purchase the items from a vendor).

However, at higher levels you may find that some purple gear cannot be modified, while orange gear can always be modified.