The intellectual refers to the one and only prototype of the class intellectual and an intellectual refers to any member of the class intellectual.
You can single out and point to the intellectual because there is only one prototype in existence. When we point to an object, we can say this or that. Old English got along fine without a definite article, using the word for that (in its many inflections) as a marker of definiteness. (See Page 86 of a biography of the English language.)
You cannot do the same exact thing regarding an intellectual because he could be one/any of many. Sure you could point to an intellectual but there are others around that you could also point to and call an intellectual.
If it helps, you can think of an intellectual as your average intellectual or any old intellectual. See Just give me one. I don't care which [one] at any old thing.
If it helps, both one and any are extremely close in etymology: any meaning one-y. See the Old English and, more to the point, proto-German words at those links.
In addition, according to many scholars, one used to be pronounced without the initial w- sound, so it sounded quite similar to unstressed an, which was the initial form of the indefinite article (later, folks dropped the n before consonants). This pronunciation, without initial w-, is retained in only.
Much of what I am writing here can apply to non-generic usages of the and a.
This question seems to follow your previous “Only the masochist would choose to study Russian” or “Only a masochist would choose to study Russian”?
. Yet as your average native speaker, I don't know why you would get this idea that you ask about here. Perhaps you could explain why you think this idea of yours might be true? What about three types of generic noun phrases (or two in this case) prompts this kind of idea?