A paint, as far as boers, is any goat that has color on at least 15% of it's body below the neck....Anything under 80% color is a paint.
Solid colors aren't really considered as paints, they're just listed as black or red as long as they are at least 80% colored. Over that, it's solid black or red.
Spotted generally means there are circular spots / splotches. Moon spots are light spots over a darker color.
Dappled means irregular shaped splotches of color mixed in the coat, and the dapples (splotches) can be a blend of other colors.
The link posted above this post has some really good examples.
With dairy goats, at least Nubians, I don't think it matters so much... I've found one person's "paint" can be another person's "black and white with tan trim".
In my Nub herd, Foxy, who would be considered "dappled" if she were a boer, was listed as "brown with multi colored spots" on her ADGA reg by her breeder.
Derri, who is very similar in color, was listed by me as "brown with tan spots and splotches".
It's *much* easier w/ the toggs and Obs who are all the same color, lol.