A cabinet has a closure like a door, a shelf is any horizontal surface for storage. All cabinets have shelves. A drawer pulls out of a cabinet, it slides out and allows you to store things like forks, knives, etc and it has an open top. I suggest you do a google image search of each word to get clarity

Shia, I agree with you. I think the original text is wrong.

A shelf can have no doors to it, as in bookshelf. Drawers fit into a 'chest of draws' or a cabinet, and are pulled out.

All cabinets have shelves? I thought (after reading your description), some cabinets have shelves, some have drawers?