I wonder in what context would people ask "How are they different?" and "How different are they?" respectively?
Such as asking about American english and British english.
And what are the likely answers to both questions?
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Sign up to join this communityHow are they different? One is red and one is blue. One is a square and the other is a triangle.
To answer this question, you explain the differences. A counterpart question might be: "... and how are they alike?"
How different are they? They are indistinguishable.
How different are they? They are almost the same.
How different are they? They are nothing alike.
How different are they? They are like night and day.
To answer this question, you rate the extent that they are different.
'How are they different?' asks for examples where (for instance 'American English' and 'UK English') differ. It is requesting a list of differences. The language enquiry may well spring from a real interest in linguistic peculiarities.
............
'How different are they?' is asking about the degree to which (for instance 'American English' and 'UK English') differ. There may in this example be a hint of the attitude 'I hope they're not that different; I don't want to have to master two new languages.'
The answers given may overlap to a large degree, as one query asks for a list ('Well, there's A, and B, which can lead to misunderstandings, and there's C and D, and then there's E ...') and the other needs to see how long that list would be (and the answerer would have to spell it out to assess its length: 'Well, there's A and B and C and D, ... er ... E ...').