What exactly is the difference between orange and purple gear?

Purple Gear is always more expensive due to being more rare (which is imho debatable when sold by a vendor, but that just as a side note).

Both, orange and purple items allow modifications to change their rating, aka item level.

But is there actually any real difference between those items as in stats when fully upgraded? Do purple items have different upgrades later on?

Solution 1:

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.

Solution 2:

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.

Solution 3:

F2P and preferred players can't equip level 50 or lower purple items without an authorization (from the Cartel Market).