Have you tried using google images and looking up, Paint boer, paint nubian, spotted boer, spotted nubian ect....
that might be easier than people trying to explain it.
A paint boer has more color on their body than the allowed tradtional boer. So even one solid brown leg, would be considered a paint. And ofcourse a solid red boer would be considered a paint. I beleive it can't have more than a 2 inch spot anywhere on its body, or it is considered to be paint, not including the tail. The tail is allowed to be colored for the boer to still be considered traditional.
Spotted is when they have smaller white spots scattered on large patches of color.
And dappled is a little harder to explain. It is more of a white under color with dapples of color through out it. Like you flung paint on a white surface.
As far as differences between breeds, I don't know if the meaning of the words change, But since there is difference in breed standards, what is considered traditional color in one breed may be considered a paint in another breed.
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.