What is the difference when you say "get off of something" and "get off something"?
I can’t speak to overseas or Canadian usage, but think there is no hard-and-fast rule in US usage. There is a tendency—and it’s no more than that—to reserve the two-place prepositions off of, down from, out of, and those with to for directional contexts, much like into, while the one-place versions are preferred in locational contexts. I, at least, tend to speak of a motion being taken off of the table; if am subsequently asked about its status, I am more likely to say “Oh, it’s off the table now.” However, other two-place prepositions are more likely to be locational: down in, up on (not the same as upon!), over at.
The two-place prepositions sometimes have an intensive sense. I tell my son “Get off your butt”; when I come back twenty minutes later and he’s still watching TV, I say more sharply “Get offa your butt!” In heated dispute I am more likely to say “Get offa your damn high horse!” than just “Get off your high horse.” But I suspect these are occasioned by prosodic rather than semantic considerations.
I take it that this question is about the use of the complex preposition off of in general. ‘The Cambridge Guide to English Usage’ says that, in such cases,
. . . one can argue that the of is redundant. Yet in American English off of appears so often in print that it has idiomatic status, and is not edited out, as in British English . . . Webster’s English Usage (1989) expresses reservations about using it in the most formal prose, but there’s no doubt that off of is thoroughly established.
The Oxford English Dictionary says that when off is followed by of, it is
In later use only colloquial (nonstandard) and regional.
'Regional' can be taken as including the United States. The Rolling Stones, of course, sang 'Hey! You! Get off of my cloud'.
The difference between them, is that "off of" is used by Americans. For English and other British people, saying "off", would be sufficient. Saying "off of", is not really necessary. It is an example of, American English involving words that are superfluous. Surplus to requirements. Unnecessary, added extras.