Generally speaking, the tl;dr to high casual as a tag.

High casual spawned [i]a long time ago in an old guild far far away[/i] because of a schism back between 2007-2008 in the advanced section. You had a bunch of elitist twats and not-so-elitist twats and the elitists often bullied or picked on those whom weren't "at their level" of writing excessive, nonsensical, incoherent ramblings for posts. Eventually they left to start their own site and it failed hilariously, they took most of the elitism with them.

"Most" being the key word. It took another year or two before the poison was really ironed out of the system by the rest of us with common sense simply ignoring the pitiful pleas from others to kick people because they [i]didn't[/i] spend fourteen paragraphs describing walking down a hallway. During this time high casual really became a thing as the interim between casual (which was swarmed with people who could barely surmount a paragraph) and those "exiled" from advanced (2+ paragraphs being their average).

Over the last couple of years high casual as a term has mutated into a synonym for quality and effort. The key word here being effort. Advanced requires things, high casual requests things, I suppose, is the main difference in thought between the two. One is inherently softer and makes a person feel more comfortable if they don't reach it, but really, what remaining elitism there is in advanced is mainly self-mocking: Egotistical twats like me tend to make fun of ourselves nowadays.

The reality of the situation now? High casual is a tag that is used to request quality role players. Since every GM in casual wants quality role players, de cream l'crop, the vast majority put it in there whether or not they understand the term or its historical connotations. Simply: High casual used to have a logical place. It no longer does really. Casual requires one paragraph or more, there are no limitations beyond that. You can write a fourteen paragraph post in casual if you want to, nothing is stopping you and unlike in Free, people will probably actually read it and admire you for the effort. Advanced requires two or more paragraphs with a good grip of the English language, though by "good grip" I've found junior high level or greater (basic grammar, intermediate literacy) tends to be passable, with high school levels being the normal level at which people write there.

The jump from casual to advanced is actually quite small now. It's basically one extra foot of water in the pool, though it looks so much scarier, in reality, it's not, really. I role play in both sections.

The real difference isn't particularly in quality nowadays so much as it is simply in style. Casual role plays tend to have a more games-like feel to them, many often incorporate classes and combat roles, or base themselves in action-oriented narratives. Advanced role plays tend to have a more novel-like feel to them, they push away the more gamey-feeling stuff to have larger and more complex plot lines with several cherishing character development and interpersonal relationships--and all the dynamics that come with that--over sheer action. You'll find more mystery plots here, or grand Tolkien-like adventures in which most of the story is not centered around combat, but instead around the evolution of the story and its characters as people and ideologies and nations collide.

The above paragraph is also self-demonstrating: The casual section gets to the point as quickly and concisely as it can. The advanced section likes to be long winded and wordy and artsy with mixed results.

EDIT

And yes. This is a tl;dr of high casual, believe it or not.