Types of Orcs
The name "Uruk-hai" has the element Uruk, which is a Black Speech word related to Orc, related to the word "Urko" in Tolkien's invented language of Quenya. The element hai means "folk", so "Uruk-hai" is "Orc-folk".
In the The Hobbit, which originally was unconnected with the The Silmarillion, he used the familiar term "goblin" for the benefit of modern readers. By the time of The Lord of the Rings, however, he'd decided that "goblin" wouldn't do - Orcs were not storybook goblins (see above).
Gundabad remained an Orc stronghold, until it was cleared of orcs in TA 2799, after the War of the Dwarves and Orcs. However, small groups of orcs must have returned and fortified it anew during the events of The Hobbit, menacing Wilderland once again.
Morannon Orcs were a type of Orc originating in Mordor, but were not necessarily all bred there at the Morannon, the Black Gate of Mordor. The term "Morannon Orc" does not originate from J.R.R. Tolkien's works.
Morgul Orcs, more commonly known as the "Orcs of Minas Morgul", were Orcs of Mordor, originating directly in Minas Morgul. History Edit. Their highest leader was the Witch-King, who led the Siege upon Minas Tirith.
"Moria Orcs" refers to the orcs who in TA 2480 came to inhabit the Dwarven realm of Khazad-dum, at the time Sauron populated "Moria with his creatures", long after the Dwarves had fled there in 1981. Three centuries later, Azog was their leader.
Uruk-hai was a Black Speech word that meant "Orc-folk". The name "Uruk-hai" has the element Uruk, a Black Speech word related to "orc" and to the (Valinórean) Quenya word urko (Ñoldorin Quenya: orko) of the same meaning. The element hai means "folk", so "Uruk-hai" is "Orc-folk".