By feel I can identify 20 lb, 24 lb, 28 lb, 65 lb cover, 110 lb cover, and 12 pt matte paper. I'm increasingly impressed by people's business cards as a result, as it is often much, much heavier than 12 pt matte.
Using comparison I can distinguish 80 lb semi-gloss cover, 100 lb semi-gloss cover, 8 pt gloss, 10 pt gloss, and 12 pt gloss. (But then again, most people could, given multiple choices rather than a free-response question.)
In case you're legitimately asking: No, it's just cheaper and fancier versions of normal printer paper and cardstock (cover and cardstock are essentially the same thing). You just feel its texture, maybe shake it a little, figure out its weight.
I worked for a few months in a print shop. Turns out I hate doing customer service, but I did take home lots of excess cardboard and paper (slightly dog-eared, bent, stained --- not professional level, but good enough for me) and bind a few of my own notebooks out of them.
To be clear, it's not my career. I'm going to school to study something else, and I only worked around 20 hours a week for about two months.