Besides a generic “Text” weight or “Cover” weight, descriptions often include a number to refer to the weight of the paper. The higher the number, the heavier the paper. Heavier paper is typically thicker as well.
There are two systems for indicating the weight of paper; an international metric system and a North American system. The North American system for paper weight uses pounds (expressed as either # or lb) while the metric system uses grams per square meter (gsm or g/m2 or g/m²), often called “grammage”. The North American pound rating is based on the weight of 500 sheets (a.k.a. a ream), while the metric rating is based on the weight of a 1 meter by 1-meter sheet.
The U.S. system is a bit confusing because the same pound number can be used for both lighter (Text) paper and heavier (Cover) paper. For example, 80# Text paper and 80# Cover paper have the same pound number even though the Cover stock is almost twice as heavy! The metric system in comparison is more straightforward. For example, 80# Text Paper weighs 104 g/m² while 80# Cover Stock weighs 218 g/m². The Cover stock is clearly more than twice as heavy as the Text stock.
The reason the actual weight of Text and Cover stock of the same pound rating will be different is due to the way the pound rating is determined. Both use the weight of 500 sheets for the pound rating, but they use a different size sheets. For Text stock, 500 sheets measuring 25″ x 38″ are used. While for Cover stock, 500 sheets measuring 20″ x 26″ sheets are used instead.