What is the difference between 差别, 分别, and 区别?

Question

All of them can mean difference. Are all of them interchangeable when used to mean 'difference?'

Answer 1

When they function as nouns to mean difference in the general sense, they are mostly interchangeable.

这两个东西的差别/分别/区别在于……

The difference between these two thingies lies in…

差别 seems to emphasize the difference itself, while 分别/区别 tend to indicate a desire to tell two different things apart (therefore the word "difference" in the title of your question should be translated into 区别). The above example sentence may have slightly different nuances depending on interpretation:

这两个东西的差别是……

What is different in one than in the other is…

这两个东西的区别是……

What distinguishes one from the other is…

BTW, although not in noun form, 差别对待/分别对待/区别对待 makes for an interesting comparison:

差别对待

to treat discriminatorily

分别对待

to treat separately

区别对待

to treat discriminatively (not necessarily with discrimination)

Answer 2

差别 means literally difference (usually as a noun)

分别 and 区别 are interchangeable, meaning to sort out to get the difference (usually as a verb)