"Different" means the same in math as it does anywhere else: "not the same as another or each other; unlike in nature, form, or quality."
"Difference" is the answer in a subtraction problem: " a quantity by which amounts differ; the remainder left after subtraction of one value from another."
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It means basically the same as outside of math. It means that two things (or some aspect about two things, such as the length of line segments or the measure of angles) are NOT THE SAME.