Brightness
Brightness is an optical quality of paper based on reflection of light from its surface. Brightness is the percentage of incident light reflected from paper when the light source is at a 45 degree angle to the paper and the measuring device at a 90 degree angle. The brightness of white and near-white papers can be considered as the whiteness of the paper as it appears to the eye. Brightness affects the contrast, color values, and attractive appearance of a printed product.

Gloss
Gloss is one of several properties of paper based on reflection of light from the paper surface. Gloss is the amount of light reflected from paper when the angle of illumination equals the angle of reflection (when the angle of the paper and light is such that the light "hits your eyes"). Gloss is perceived as the shiny or lustrous appearance of paper. To compare the gloss of two different sheets, put one sheet over the other halfway so you have the surfaces of both exposed. Hold these sheets up to a light source and angle the sheets around until the light reflects brightly to the eye from the paper. You will see a streak of shiny gloss going across both sheets and can easily see which is glossier.  

Caliper
Caliper is the THICKNESS of the paper as measured in 1/1000's of an inch. 10 point is .010 inches thick.

Basis Weight
The Basis Weight, or weight, of paper is the number of pounds that 500 sheets of a certain size weighs. That "certain size" is specific to a grade of paper. For example, Cover is measured in size 20 x 26, SBS or Tag is measured in 24 x 36, Offset and Litho is measured in 25 x 38, and bond or "Sub" weights are measured in 17 x 22. Roll items are sometimes expressed in MSF.

Finish or Smoothness
Finish is the smoothness of the paper surface. The Sheffield Smoothness test measures the amount of air that escapes when a Sheffield tester is pressed flat against the paper and air is blown out. The less air that escapes, the smoother the paper is. Therefore, the lower the Sheffield Smoothness, the smoother the paper is. Finish can also refer to special embossed finishes. The finish of uncoated paper is customarily described as Vellum (rough), Smooth (smooth), or Supercalendared (high "polished" smoothness).

Grain
The Grain direction is the direction that most of the paper fibers lay longitudinally in a sheet of paper. The paper fibers lay parallel to the direction in which the paper is made on the paper machine. You can determine the Grain Direction of a sheet of paper by comparing the flexing resistance of the sheet in the East-West direction versus the North-South direction. The direction which offers the least resistance is the grain direction.

General Principle in Paper Manufacturing
You can change 2 of the following properties of paper and must allow the third to float: Weight, Caliper and Smoothness.