Most of the terms used to describe paper weights in the United States refer to the "Basis Weight" of the paper, not the actual thickness or feel of the paper.
Basis Weight is the weight in pounds of a specific number of sheets (usually 500) of paper in a specific size. Unfortunately, most of the different paper weight classifications use different size sheets of paper so they cannot be directly compared. This is why 80 lb. Text and 80 lb. Cover papers are not the same thickness.
Text WeightDescription: Lightweight paper commonly used for letterheads, notepads and envelopes
Basis: 500 sheets @ 25 inches x 38 inches
Bond WeightDescription: Heavier than Text Weight - strong, stiff paper often used for letterheads
Basis: 500 sheets @ 17 inches x 22 inches
Cover WeightDescription: Heavyweight paper used for postcards and business cards
Basis: 500 sheets @ 20 inches x 26 inches