Grammage and basis weight, in the pulp and paper industry, are the area density of a paper product, that is, it is mass per unit of area. 

Grammage

In the metric system, the mass per unit area of all types of paper and paperboard is expressed in terms of grams per square meter (g/m2). This quantity is commonly called grammage in both English and French. 
ISO 536:2019 — Paper and board — Determination of grammage.

Basis weight

The following description comes from Wikipedia:

In countries that use American paper sizes, a less verifiable measure known as basis weight is used in addition to or instead of grammage. The basis weight of paper is the density of paper expressed in terms of the mass of a ream of given dimensions and a sheet count. In the US system, the weight is specified in avoirdupois pounds and the sheet count of a paper ream is usually 500 sheets. However, the mass specified is not the mass of the ream that is sold to the customer. Instead, it is the mass of the uncut "basis ream" in which the sheets have some larger size (parent size). Often, that is a size used during the manufacturing process before the paper is cut to the dimensions in which it is sold. So, to compute the mass per area, one must know

• the mass of the basis ream,
• the number of sheets in that ream, and
• the dimensions of an "uncut" sheet in that ream.

The standard dimensions and sheet count of a ream vary according to the type of paper. These "uncut" basis sizes are not normally labeled on the product, are not formally standardized, and therefore have to be guessed or inferred somehow from trading practice. Historically, this convention is the product of pragmatic considerations such as the size of a sheet mould.

By using the same basis sheet size for the same type of paper, consumers can easily compare papers of differing brands. Twenty-pound bond paper is always lighter and thinner than a 32-pound bond, no matter what its cut size, and 20-pound bond letter size and 20-pound bond legal size papers are the same weight paper with a different cut size.

However, a sheet of common copy paper that has a basis weight of 20 pounds (9.1 kg) does not have the same mass as the same size sheet of coarse paper (newsprint). In the former case, the standard ream is 500 sheets of 17-by-22-inch (432 by 559 mm) paper, and in the latter, 500 sheets of 24-by-36-inch (610 by 914 mm) paper. Here are some basic ream sizes for various types of paper. Units are inches except where noted.

Paper type	Paper size (inches)		Sheets per ream
Bond, writing, ledger	17	× 22	500
Manuscript cover	18	× 31	500
Blotting	19	× 24	500
Box cover	20	× 24	500
Cover	20	× 26	500 or 1000
Watercolor	22	× 30	500
Bristol and tag	22+1⁄2	× 28+1⁄2	500
Tissue	24	× 36	480
Newsprint	24	× 36	500
Hanging, waxing, bag, etc.	24	× 36	500
Book, text, offset	25	× 38	500
Index bristol	25+1⁄2	× 30+1⁄2	500
Paperboard (all types)	12	× 12	1000 (1000 sq ft per ream)

Sheets 17 by 22 inches (432 by 559 mm) can be cut into four 8+1⁄2-by-11-inch (216 by 279 mm) sheets, a standard for business stationery known conventionally as letter sized paper. So, the 17-by-22-inch (432 by 559 mm) ream became commonly used. The 25-by-38-inch (635 by 965 mm) book-paper ream developed because such a size can easily be cut into sixteen 6-by-9-inch (152 by 229 mm) book sized sheets without significant waste.

Early newsprint presses printed sheets 2 by 3 feet (610 by 914 mm) in size, and so the ream dimensions for newsprint became 24 by 36 inches (610 by 914 mm), with 500 sheets to a ream. Newsprint was made from ground wood pulp, and ground wood hanging paper (wallpaper) was made on newsprint machines. Newsprint was used as wrapping paper, and the first paper bags were made from newsprint. The newsprint ream standard also became the standard for packaging papers, even though in packaging papers kraft pulp, rather than ground wood, was used for greater strength.

Paper weight is sometimes stated using the "#" symbol. For example, "20#" means "20 pounds per basis ream of 500 sheets". When the density of a ream of paper is given in pounds, it is often accompanied by its "M weight". The M weight is the weight (in pounds) of 1000 cut sheets. Paper suppliers will often charge by M weight, since it is always consistent within a specific paper size, and because it allows a simple weight calculation for shipping charges.

For example, a 500-sheet ream of 20# 8+1⁄2-by-11-inch (216 by 279 mm) copy paper may be specified "10 M". 1000 cut sheets (or two reams) will weigh 10 lb (4.5 kg), half of the four reams of cut paper resulting from the 20# basis ream of 17-by-22-inch (432 by 559 mm) paper.