should we say, "what's different between objectA and objectB"
or "what's difference between objectA and objectB"
With the second, say 'what's the difference...'
I think "what's different" is by far less idiomatic (i.e. less common).
Additionally, "different" is an adjective and "difference" is a noun. Nouns take require a deteminer, either "a" or "the". "Adjectives" pair up with the verb TO BE (is, are, am, and so on).
[1] Determiner + Noun
Q: What is the difference between A and B?
A: The difference is this, A is longer.
[2] Adjective + Noun
Q: What difference is there between A and B?
A: There is a marked difference between A and B.
[3] to be + adjective
Q: What is different between A and B?
A: A is longer.