[Firefoot]

A couple of pieces:

"Most of the Orcs of the Misty Mountains were scattered or destroyed in the Battle of Five Armies."

A Journey in the Dark, FotR

Obviously, they're pretty much just called Goblins in TH.

Azog caem forth, and he was a great Orc...

Appendix A, III

"Thror was killed, you remember, in the mines of Moria by Azog the Goblin."

An Unexpected Party, TH

This same guy is called both an Orc and a Goblin - and he's a big Orc, too, so I don't think you can argue Goblins are smaller.

I don't think that a strong, text-based argument can really be made for Orcs and Goblins being different.

What was the Great Goblin that recognized Orcrist and Glamdring? Thats as about as close as I saw in his works to a Goblin (orc) king, other than Bolg who led the Goblin Army in the Battle of Five Armies, but Bolg was just the leader (or the strongest goblin), not necessarily a king. Is that right?

The Great Goblin appears to be a king, even if not in name (I don't remember if he's ever called that or not). But it seems fairly typical that where Orcs/Goblins are living on their own (i.e., not as Sauron's/Morgoth's slaves), they have some sort of leadership - The Great Goblin, Azog, Bolg - there even seems to be some kind of history behind Shagrat and Gorbag where they were some kind of leadership. And I think that Ugluk would be somewhat of a leader whether or not he was made so by Saruman.