Both "What is the difference between X and Y?" and "What are the differences between X and Y?" are grammatical and will be understood.
According to my native-speaker intuition, "What is the difference ...?" is the normal phrasing. I would only use "What are the differences ...?" if I was already pretty sure that there was more than one difference.
Some additional cases that came up in the comments:
The labels "X" and "Y" will, of course, always be different, but that does not count as a difference between the things X and Y, and therefore is not a reason to use the plural form. The answer to "What is/are the difference/s between ice cream and ice-cream?" would be "There is none, they are the same thing."1
"What is a difference between X and Y?" is also grammatical, but it means something that one hardly ever wants to say: the speaker has deliberately refused to indicate how many differences he or she thinks there are, and no matter how many the listener thinks there are, the speaker only wants to hear about one of them. The only time I personally would use this variation is if I was writing an exam question.
"How do X and Y differ?" is an alternative phrasing that avoids the question of number altogether; unlike "What is a difference...", it carries no special connotations.
1 Consider also tomAYto versus tomAHto. You might find it helpful to read up on the use-mention distinction.