To differentiate is a VERB meaning to make/see a difference "Can you differentiate between the two twins?" Difference is a NOUN "there is a big differeence between those two boys". Hope this helps.

To "differentiate" means to tell the "difference" between two things. Here's an example---> A teacher says, "Class, for this assignment, I want you to differentiate between a bat and a bird." Tommy doesn't know what the teacher means, so he asks, "What do you mean, 'differentiate'?" The teacher smiles and says, "Tell me the difference between a bat and a bird."

When you come across the expression 'differentiate between A and B' it implies that it is not obvious, that it could be difficult. For example 'I am able to differentiate between different accents in English easily enough, but I could not differentiate between Mandarin and Cantonese.' 'Can you differentiate between [tell the difference between] the twins Billy and Johnny ? - they look the same to me !'