Pantone makes ink. Physical, printing-press, oil-based inks in many colors. They publish a guide to choose ink colors. They publish physical swatchbooks as well as electronic files that Adobe uses in their softwares.
Solid inks are premixed inks that are the right color right out of the can. Trowel it into the fountain on a press and you have color match without fail.
A four-color process color is built-up on press by laying down amounts of CMYK, Cyan ink, magenta ink, Yellow ink, and (K)Black ink. From these four inks, you can simulate a whole gamut or spectrum of color. For example, if you print dots of cyan blue ink amongst dots of yellow ink, you achieve the visual appearance of green. Yet it is not green ink. A Pantone solid green would really be an ink premixed to a hue of green. On press, one solid ink would be applied versus 2 to 4 of the process CMYK inks being printed to simulate the same hue.
The term coated or uncoated refers to the kind of paper you are printing the ink upon. Coated stocks of paper are wood fiber compounded with clays to achieve a very dense, shiny surface. The ink tends to lay on top--not wick in--and so the coated stock printed piece looks shinier.
Uncoated stock, such as newsprint paper, has no clay in the paper, and allows ink to soak into the wood fiber of the paper. The result is far less shiny--duller of specularity than coated stock.
Bear in mind that process simulations of Pantone ink colors can never exactly match the hue. They can only get near, so don't expect to match Pantone solids in the process version.
Mike Witherell in Washington DC