I've been to another RP site where they actually distinguished RPs on a scale of how much effort you would be expected to put into them. "Casual" meant minimal SUs, not too advanced settings and plot and one liners being okay, while "Advanced" meant proper background, detailed SUs and long, well written posts. Here, we mostly lean towards their Advanced definition, I'd say.
I believe I know the site as to which you are describing. But this "Casual" and "Advanced" means more, and somewhat different, to what you have described.
"Free" means "one-liners." This does not mean they always or can only write one liners. There is virtually no minimum for a valid post. RPers who don't care to develop plot, character, or setting (I'm not saying they don't do any of the listed items). It's pretty much IMing as a fictional character via forum. However, it also means there are no standards for grammar. It's also very fast-paced and live only as long as you are online at that particular time (this is not always the case). CS's (Character Sheets or the term I use to describe this site's "Sign-ups") are optional and tend not to be made. People will say "I want to join" in the Interest Check/Out-of-Character and then write in the In-Character.
"Casual" means "a paragraph." The minimum is a paragraph but most write more than that on a regular basis. Grammar is also noted, but not necessarily stressed. RPers work toward working through a story with their characters. It's not necessarily to the level of writing a novel between multiple people at this level, but it's much more involved and deeper than that of "Free." CS's are moderately detailed (I'm not indicating to length, since that is up to the GM and the RPer in question).
"Advanced" means "three paragraphs." The minimum is a paragraph of a mental reaction, then a physical reaction, then a mental reaction to that same character's physical reaction (or this is just how I would describe the minimum). Grammar is stressed, here. RPers work together with GMs to create a larger world (the good RPs, at least). They create species, magics, continents, cultures, sociologies, medicines, etc. This can occur in "Casual," but not nearly the same extent. CS's, here, can be at the level of "Casual" to entire biographies. I know on the site I believe you referenced, there are debates on what is necessary to include in a CS (which I won't get into here), which can affect how long a CS required by the GM might be.
But, overall, if we had these systems/tiers of RPs, then it would be difficult for Moderators to moderate and there would be too much variance in the definitions of these terms. Players will become offended and GM's will be alienated or victimized, unless properly moderated and terms definitively defined. Advanced will become scary and Casual will be over-saturated.
But it really all depends what we want this particular RPing section of the larger forum as a whole to be. I'm, pretty much, a strictly "Advanced" RPer (according to my definition above), and don't care to even have to skim through "lower tiered" RPs. I know that sounds elitist, but I'm just lazy. I'm also pretty strict with grammar, so it bugs me when I'm correcting your post rather than reading it (because there are that many errors).