Are those verb have to same meaning? When should I use which?
Have you checked your dictionary?
Differentiate means: to recognize or ascertain what makes someone or something different. Example: Children can differentiate the past from the present.
Differ means: to be unlike or dissimilar. Example: The second set of data differed from the first set.
My pleasure, and enjoy your vacation.
When you are away from your dictionary, you can always go online (as you obviously are at the moment) and check one of the excellent dictionaries there.
Dictionary.com | Find the Meanings and Definitions of Words at Dictionary.com is a good one, as is www.oxforddictionaries.com