What is the difference between "aged" and "age"?

Aged means that the person or people you are referring to is/are of the given age. It's always referring to someone. In this case what follows the verb to be is an adjectival phrase acting as a complement, and since it is talking about the subject, it's specifically called a subjective complement. But the important thing is that the main form of [aged 12] is that of an adjectival phrase.

The boy is aged 11.
I'm aged 20.

Aged can usually be replaced with of age:

The boy is of age 11.
I'm of age 20.

Now, when talking about age alone, age is a noun and [age 11] is a noun phrase. In the case of your examples, [college aged students] and [college age students] represent two different cases of noun modification.

[College aged] is clearly an adjectival phrase.
[College age] is clearly a noun phrase.

In the first case, [[college aged] students] you are modifying a noun [students] with an adjective, which is correct.

In the second case, [[college age] students] you are modifying a noun [students] with another noun, which is also correct.

Summing up: for the specific case of the question, it would be the same and would have almost the same exact effect to use either [college age students] or [college aged students].

Per the Macmillan dictionary, aged is an adjective:

aged, adj. : someone who is aged 18, 35, 70, etc. is 18, 35, 70, etc. years old

A woman aged 50 has given birth to twins.

Men aged between 18 and 35 are most at risk from violent crime.

In the second case, a group of students that are of college age are college age (not college aged) students. Note the preponderance of college age over college aged in the literature: