Use "distinguish between" when you are making a comparison. To set up a comparison you should either use "between" or say something like "distinguish A from B" or "distinguish the objects from each other". If you don't explicitly set up a comparison in one of the above ways, "distinguish" does not necessarily set up any comparison. It can refer to just one thing. For example, "I could distinguish his face in the dark". You CAN use it for a comparison, but it is clearer if you set up comparisons explicitly.