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I just got an email from my school saying that I need to fill out a form requesting my refund.
What do they mean by refund? Are they referring to the money that I was approved for beyond tuition costs?

Most likely. Many schools use a form to determine how to release your funds (the cost of living money left over after tuition and fees are paid). Either they cut you a check or direct deposit the $ to an account of your choosing.

Yes, they are talking about anything you received in excess of tuition. At Michigan they make grad students fill out an employment form at the payroll office if you want it direct deposited.