Uncoated and coated paper: have different surface textures. In the papermaking process, uncoated stock has been compressed between metal rollers to a limited degree, yielding vellum, antique, wove and smooth surfaces (from rough to smooth, depending on the amount of compression). Coated paper varies from roughest (matte) to smoother (dull) to smoothest (gloss), also depending on the amount of compression. Paper can also have such textures as "linen" and "canvas" pressed into the surface. Generally, the smoother the surface, the better holdout a sheet has (the better the ink sits on the surface of the paper rather than being absorbed into the fibers).
M Weight: is based on the physical weight of 1000 sheets of paper. For example, 1000 sheets of 80# cover, measured at 20" x 26", weighs 160 pounds. The same paper in text weight still weighs 160 pounds but the sheet size is larger at 25" x 38", making it a thinner sheet. Most paper weights in printing fall into the areas of bond (lightest weights), text (light to medium weights) and cover (heaviest weights).
Opacity determines show-through. A sheet with high opacity will prevent solids, screens and halftones from being visible through the opposite side of the sheet. Colored sheets are usually more opaque than white sheets. This quality is rated on a 1 to 100 scale. Most sheets fall in the 80 to high 90 range.