The above information is good, but I'll just add a bit to explain why some collectors are fussy about making the distinction. It all has to do with who the artist is. This info is from
an interesting insider's description of the animation process by Jan Frazier, who often puts in appearances at Katsucon.
First of all, there are two preliminary steps:
1. Storyboard (usually done by the series or episode director). These are very precious, and generally the only form in which you find them in in the photocopies made by the studio and circulated among the various artists.
2. Layout (usually done, so far as I can tell, by the director, though Frazier says that some are also done by key animators). These are very rough conceptions of where characters will appear on the screen. Often you get these with production backgrounds.
Then you get the steps described correctly by EoP in the post above:
3. Rough (sometimes called "correction layout): these are, for me, the most desirable, as they are usually in the hand of the episode's animation director. They can be extremely beautiful or very preliminary (and I've seen the term "genzu" or "exploratory drawing" to refer to these "rough roughs). Anyhow, this sketch records the moment when the image that ends up on screen is created; everything afterwards is clean-up and refinement.
4. Genga ("original or foundation drawing"): these, according to Frazier, are drawn by "gengamen" (though some are women), who are senior animators assigned to the "key" or most important moments in the scene. A genga set is incomplete, since it only defines the beginning, end, and critical positions of the characters' movements.
5. Syuusei or Shuusei ("correction"): these are again done by the animation director. In most cases they are partial, only cleaning up the bits that the animation director found faulty in the gengaman's work. But I have seen some lovely complete shuuseis where the director completely replaced the gengaman's drawing with one of his/her own.
6. Douga ("animating drawing"): these are traced versions of the key gengas, along with "inbetweeners" that link the genga images smoothly. These tracings eventually are transferred to the acetate on which the cel is painted or scanned to be colorized by CGI artists. Quoth Frazier:
Inbetweening is a relatively non-creative job. It is more tracing than anything else. The hours are long and the key animators are sometimes very hard to work with. The cruelest part of being an inbetweener is that they rarely get to work on anything they are fans of and what they do get to work on they burn out on quickly. [...] After 2 or 3 years of grueling inbetweening, animators who can handle it are usually promoted to keys.
Gengas have the key number written on the sketch beside the character; dougas have the sequence number written in the upper right corner (or sometimes, for oversized images, in the lower right corner). The ones that are traced from the key gengas have the numbers circled. This is how you can tell that a cel painted from that douga is a "key," i.e., an image directly based on a senior animator's genga, as corrected by the animation director's shuusei.
Cels, btw, tend to be painted in sweatshop circumstances and their artists are among the lowest paid and least creative in the process. Hence, while they are visually the most compelling art that comes from the animation process, they are actually the object that involves the least amount of creative artistry. That's why some of us develop a thing for roughs, gengas, and shuuseis, even for shows where cels are also available, because they are the most tangible products of the talented artists who actually created the anime.
A lot of info: but if you look at a lot of this kind of art, you'll soon begin to appreciate it, as well as the immense amount of work that goes into even the simplest animated scenes.