Well, if I remember correctly, I think that goblin is used earlier on and eventually stops being used in favour of orc. And yes, it is mostly used in relation to Hobbits.
I think the word goblin is used to show the orcs as creatures of legend which the Hobbits know only from stories, and so the reader can relate to it as a distant tale. I don't think that anyone other than the Hobbits ever use it in LOTR, and it fades out in narration as well.
This is probably because by this time, they are faced with the reality of the orcs, and hear everyone talk of orcs, so that makes the reader see them as what Tolkien wants- People already have images in their minds of goblins, and so do the hobbits probably, but with the word orc Tolkien makes them his own.
And since it is Frodo writing this, and we see him becoming less and less hobbitish throughout, I think this is a sign of him being more aware of the real world, and seeing orcs as living beings rather than just stories. And when they are real they are referred to as orcs by everyone else, so that is the name.
The hobbit is much more fairy-tale-ish, so I imagine the the word goblin is more appropriate here, whereas LOTR deals with the grimmer, harsher reality and so uses the word which they were called at the time, as goblin would make them seem less real. The word orc itself contains harsher sounds than goblin anyway, and we know that Tolkien thought a lot about the sound of words.
So in summary, I think that the change of the word goblin progresses into the word orc to show the change in Frodo, and his attitude towards them. I agree with Galin about orc being the Westron term, especially as it is so close to the Sindarin orch.
As a linguist, I'm sure Tolkien was aware of each, and that goblin already evokes certain images, whereas orc, (for most people, at least) is something entirely new and exciting and is what Frodo has to face (not the goblins of tales, but the living, breathing, fighting orcs).
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