Different from means not the same.
e.g -- Sara's taste is different from mine.
Different than -- In US English, than is an alternative to from before a clause.
e.g -- Sara's appearance was very different than I'd expected.
NOTE : On GMAT different than is generally always wrong when comparing two nouns. Different than is only correct when a sentence compares a noun and a clause.
Hence if on GMAT sentence correction you come across a question comparing two nouns and choice with the word different then look for a choice without the phrase different than