The term Orc does occur twice; once in an instance where Gandalf is trying to scare Bilbo by mentioning creatures of the wilderness "goblins, hobgoblins, and orcs of the worst description," and again when the narrator mentions Orcs as nothing but large goblins, as well as in the Elvish name of Thorin's sword, Orcrist.
In The Lord of the Rings, Orc is used predominantly, and goblin appears mostly in the Hobbits' speech. The second volume of the novel, The Two Towers, contains passages where the more generic 'goblin' is used to describe Saruman's Uruk-hai as being different from the usual 'Orc':
There were four goblin-soldiers of greater stature, swart, slant-eyed, with thick legs and large hands. They were armed with short broad-bladed swords, not with the curved scimitars usual with Orcs: and they had bows of yew, in length and shape like the bows of Men.
Upon a stake in the middle was set a great goblin head; upon its shattered helm the white badge could still be seen.
The "white badge" mentioned in the latter passage makes it clear that the beheaded goblin was one of the Uruk-hai. Tolkien writes that these bore a white Elf-rune with the value of "S" on their helmets.
Tolkien also wrote the following note, appearing in some editions of The Hobbit:
Orc is not an English word. It occurs in one or two places but is usually translated goblin (or hobgoblin for the larger kinds).