Distinguished between Vs Distinguished from

It's debatable. What is generally agreed is that both are correct idioms. When the GMAT tests idiom, the split will be between a correct idiom and unacceptable idiom(s), not between a correct idiom and a "just OK" idiom. So, in my opinion, you won't see a GMAT question that boils down to this very fine distinction. Look for other splits in such a question.

I think you distinguish between X and Y when you list and contrast qualities of both X and Y. You distinguish X from Y when you cite qualities of X that make it unique from Y, where Y is used as the baseline or frame of reference.

Another way to put this: You distinguish between X and Y when it's all about the differences between X and Y. You distinguish X from Y when they are similar, but there's some way to tell them apart.

Examples:
Dr. Leopold distinguishes between Fuji apples and Granny Smith apples in his book, providing tips on how to grow, purchase, and use each type.
Chef Leopold distinguishes Fuji apples from other apples in his cookbook, writing that the high sugar content and dense flesh of Fuji apples makes them the best apple for baking.