Short answer:
Different to and different than are perfectly fine, but some people consider them wrong, so different from is the safest choice.
Some careful English speakers consider different to and different than problematic. The argument is that things differ from each other, and they don’t differ to or differ than each other, so different from is the only logical construction. But there are problems with the arguments against different to and different than, and the old prejudice against these phrases should be laid to rest.
First, one point in favor of different to and different than is that these constructions are common and have been common for centuries. They have appeared in works of great writers and can be found in books from editorially fastidious publishers, and no English speaker has trouble understanding them. Different than, which is especially common in the U.S., appears about twice for every three instances of different from in 21st-century newswriting from the U.S. and is common (though less so) in American books from this century. Different to, meanwhile, is nearly as common as different from in recent U.K. newswriting and is easily found in U.K. writing of all kinds not just from this century but from as long ago as the 18th century.
Plus, the argument against different than in particular is not well founded. Granted, than typically follows comparative adjectives (e.g., brighter than, less easy than), of which different is not one. This is not a rule, though, and than would not be the first word in English to have multiple uses. But the than in different than doesn’t even need to have its own definition. The word primarily means in comparison to or in contrast with, and these senses are perfectly in keeping with the word’s use in different than.
We could make similar arguments about different to. To, a versatile preposition, has numerous definitions (the Oxford dictionary lists a few dozen), several of which could be used to justify its use in making comparisons and drawing contrasts.
Different than also aids concision. Consider the sentence, “He is different than he was yesterday.” People who are very strict about these things might find fault with that sentence, yet it is more concise than the alternative, “He is different from how he was yesterday.” Also consider the sentence, “The movie had a different meaning to me than to him.” It would be possible to rephrase this sentence to use from instead of than, but all the alternatives would be wordy.
No matter what we say, however, keep in mind that there are people who consider different than and different to unequivocally wrong, so it’s a good idea to approach these phrases with caution in writing for work or school.
Adverbial constructions
Much of the above extends to adverbial constructions such as differently than and differently to. Both are common, yet some people consider them wrong.
Again, than constructions promote concision, especially when introducing independent clauses—for example, “You sing differently than I do,” is more concise than the from alternative, “You sing differently from how I sing.”
Examples
Here are some examples of different than and different to constructions in action over the last two centuries:
“Such fickleness! Oh! How different to your brother and to mine! I really believe John has the most constant heart.” [Northanger Abbey, Jane Austen (1817)]
On other minds this circumstance might have operated far differently than it did on the mind of Captain Hardinge. [The Naval Chronology of Great Britain, James Ralfe (1820)]
You stood opposite to me in the bright firelight with a face changing and flushing like a girl’s, and a happy youthful buoyant gladness in it very different to your usually quit aspect. [Mrs. Lirriper’s Legacy, Charles Dickens (1864)]
And, when I looked at him now, it was plain to me that he was of a race different to my own, just as he had always seemed different from any other man. [The Inheritors, Joseph Conrad and Ford Madox Ford (1901)]
f the object of the Grand Duke Nicholas was to attack Cracow frown the south his position will not be very different than it was when Przemysl fell. [New York Times (1915)]
He did not look very different than usual. [Islands in the Stream, Ernest Hemingway (published 1970)]
People they spoke to there described what happened in the shootings differently to how the army did. [BBC (2005)]
An Iranian representative said it was no different than his country using the IPU forum to call for international support of Quebec independence. [Globe and Mail (2012)]