Is it correct to say “different between”?

No, “different between” is usually incorrect.

Use “difference between” when comparing two or more things.

Correct:
What is the difference between “different” and “difference”?

Incorrect:
What is the different between “different” and “difference”?

Use different from, different than, or different to when describing one thing as unlike another.

Correct:
This word is different from that word.