Do both constructions mean the same? And is the first one grammatically correct?
What is the difference of x compared to y
What is the difference between x and y
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A difference of is used to indicate the extent of a difference; it's a measure, whether a degree (temperature), a metre (length), a litre (volume) or a kilogram (mass).
There is a difference of half a litre between the capacity of the two jugs.
There is a difference of nearly a centimetre between the lengths of the tables.
A difference between is used to compare two creatures/objects directly.
There is a slight colour difference between the two vases.
There is a marked difference in character between the identical twins.
There are two perspectives for describing a difference. Say you are comparing two items, A and B, that are different. Visualize:
[item A] <--difference--> [item B]
You can express it in terms of the items. In that case you describe it as the difference between A and B. (That doesn't refer to the literal position of the word in my diagram, it refers to the comparison of one to the other.)
Or having already made the comparison, you can ignore the items and talk about the difference, itself, In that case, you describe it as a difference of X.
Q: "What is the difference between 3 and 5?"
A: "The difference is 2", or "It is a difference of 2."