A mathematical set is a collection of numbers or objects, called "elements." Two sets identical if they contain the exact same values, just with different frequencies. There is no order in a set, and duplicates are not counted.
In contrast, in a list of numbers, the order of the entries matters and we count repeated elements as separate elements.
You can see ETS's own explanation here:
Two lists with exactly the same numbers but in different order can be considered different. However, the mean, median, mode, range, and standard deviation of the two lists will be exactly the same.
On the GRE or GMAT, when we're referring to "data sets" or a "set of data," we say "set" but we're not referring to a mathematical set. Really, we're actually talking about a list of numbers!
Given mathematics is strict discipline with black-and-white rules, it seems a bit silly that we can use "set" to mean different things, doesn't it?!