You have the concepts pretty nearly correct, but it's crucial not to obsess on the terminology (which varies quite a bit from US to Japanese studios) and keep your eye on the production process that generates all these drawings for very different and specific purposes. A good general introduction to the process, by an American who worked for an anime studio in Japan is
Various Positions in the Anime Industry.
A very brief summary:
1. When an anime series goes into production, the episode director (or someone under his/her direction) does a storyboard for the whole episode.
2. This becomes the basis for a series of
layouts, done to a standard size and usually on pre-printed paper with the studio's logo on the bottom and a series of blanks on the top for series title, episode, and cut (individual animated series of "shots" in US terminology). Jan-Scott Frazier thinks the key animators do this job, but I don't think this is always true. Some layouts are pretty good artistically, but most are very crude, suggesting that the director, or the director's cousin who needs a job, does no more than place the characters very approximately in the frame.
3. The layouts go to the art director, who might make a more detailed drawing of the background before sending this material to the person who executes the original production watercolor. So the autograph layout usually comes taped to the back of the original matching background.
4. A photocopy of the layout goes to the episode's animation director, who makes a revision showing more precisely what the characters should look like. This is, to many collectors' eyes, the most valuable type of sketch, as it records the "moment of creation" when the basic design of the scene is worked out. It's common to call this sketch the "
rough," although it's also referred to as a "layout correction." It's always done on some kind of thin colored paper (usually yellowish).
5. The copy layout and rough(s) go to the gengaman, or key animator, who creates the
genga, or "foundation drawings." These are limited to just the most important moments in the cut, typically the start (A1) key, the end key, and the extreme positions of any moves that take place. This is also when the cut gets taken apart into layers, so the genga will have notations beside the character indicating (say) that the body will be on the A1 layer, the eyes on a B1 layer, and the mouth on a C1 layer, etc. There are usually a lot of notes alongside the characters explaining how this character will actually be animated.
6. The genga go back to the episode's animation director for approval. Normally, the AD takes another sheet of colored paper and traces on it the parts s/he wants revised. Sometimes, the senior artist will reject the genga and do a complete new drawing expressing what s/he wants. All these post-genga drawings are usually marked "
shuusei" or "correction," and that's what collectors usually mean by that term, although I've seen animators write the word on pre-genga "layout corrections" too.
7. This whole pack of material goes to a howling mob of entry-level animators with aspirations of becoming the next Miyazaki. They trace the genga or key drawings on a sheet of white paper using a very fine pencil, then mark highlights and shadows with colored pencils, again, very precisely. Then they create a certain set of "inbetweener" images that flow together with the keys to create the image of motion. These are the
douga or "moving drawings." Because they are designed to be photocopied onto the back of sheet of acetate (or, nowadays, scanned and digitally colorized), there are no comments on the sheet itself, and the sequence number is put in the upper right or lower right corner (for oversized cels) so it is not part of the image copied on the cel or scanned for colorizing.
At this point the sequence numbers change: the genga are numbed 1, 2, 3, etc., but when the inbetweeners are added, the image in (say) the genga for A3 might now be numbered A12 on the douga. (You can see all of this worked out if you get the timing sheet with the sketch pack.) So to help keep track of how the genga and douga relate to each other, each douga that matches a genga has the sequence number circled. So a cel painted from a douga with a circled sequence number is a
"key cel" because that image is based on one actually drawn by a senior animator. A cel with a douga whose sequence number is not circled is an
"inbetweener" designed by a junior animator working for peanuts. (But Jan Scott-Frazier observes that the senior animators looked at these douga and paid attention to the artists who did the best jobs, and so these people were more likely to get the nod to be key animators for the next project.)
So when you get a "sketch pack" for a cel-based series, it's likely to have in it a copy layout, a rough or two, a set of genga, and a set of post-genga shuusei. A sketch pack for a CGI-based series will probably have the original layout, a rough, a set of genga and post-genga shuusei, plus the complete run of douga, and, if you're lucky, the timing sheet that binds them all.
That leaves "
genzu," which is just a catch-all term for any kind of practice or conceptual drawing that doesn't have a specific purpose. My impression is that these are rough drafts or what American animators call "clean-up" drawings made by an artist prior to finalizing the art in the form of a genga. As different artists have different styles and quirks, they can be very different, even within a single studio or show. Some may have the key number on them, most don't, and they can be on whatever paper happens to be around to recycle, white, colored, leftover layout stock. (Some of my
xxxHolic genzu are on the back of layout stock from a different studio with which the producing studio had recently collaborated on a project.)
I enjoy getting hold of them but it's true that they can be very difficult to interpret because they usually come separated from the more formal drawings that were used in production. I think in many cases they are just the contents of an animator's trash can that the artist (or the custodian) slipped out of the building after hours. In some cases, the studios released the production art for sale to collectors, and in others they did not, so genzu are the only art you can get from some series.
As for the links you gave,
this one looks to be a copy of what I'd call a "layout correction" rather than a rough or a layout. Notice that the artist wrote out the heading at the top and did not include the cut number. Toei promoted it to layout status later by stamping the series title (Sailor Moon, obviously) and the episode number on it. It is executed on Toei's standard layout stock, but it looks very odd to me.
This one looks to be a douga rather than a layout. Notice that it has the sequence number (A1) circled in the top right corner. It does look like it's been marked up after it was used to print the outline on the back of the cel, probably as a guide to the cel painter. The frames on it look to be a guide to some kind of panning effect used in filming the cut, and might have been done later as a guide to the cameraman. If this is from Sailor Moon too, keep in mind that Toei always used a layout frame with rounded corners, as seen in the other scan, rather than one with square corners.
This one looks very similar to a batch of genzu I got from
Inuyasha that I now think mostly dealt with deleted scenes. In any case, it shows a very preliminary approach to the character that I'd guess was cleaned up in a following sketch and then copied onto a genga. But without having the other sketches for comparison it's hard to tell.
Hope this helps. Really the only way to get a handle on this is to collect sketch sets and then spend a couple of days puzzling over them, comparing them to each other and looking at details that show you which had to come first, then later, then last. That, and a little first-hand information from people like Frazier, will eventually make sense out of the standard process. But keep in mind that there were obviously special circumstances that affected many series and many scenes, and some of these you may never figure out unless you'd been lucky enough to be in the studio on that day.