"Different from" is considered to be more standard, though "different than" has been used for decades, including in formal situations.
The proscriptive rule is that "than" is only used with comparative adjectives and "different" is not a comparative adjective, therefore "different from" is correct.
This recipe is different from the one I followed last week. They're all different, but some are more different than others.
In the second sentence, "more different" is a comparative adjective, so "than" is used.
This post was edited by Benedict Arnold at May 3, 2021 10:41 AM MDT