I feel it is now some sort of dogmatically argued issue where there just will be no agreement between the two sides. Sure, mathematically the puzzle definitions are isomorphic, but Corral (originally "Bag" until renamed for the 2002 US Qualifying Test) is a loop puzzle, and Cave is a shading puzzle. The two just can't coexist in any solver's mind. I've found I clearly solve it as a shading style, with identical notation to most other shading styles, and therefore professionally I have chosen "Cave" as the name I use for this genre. No loops needed.
But, if "Cave" is controversial to you, we can reengage in the flame-war over here if you want. Instead I wanted to offer a gift to you, Corral fans. It seems you loopers just see the world differently. So I wanted to repackage my favorite shading puzzle style for you to better enjoy. It's a style I dare not name as you probably don't like it at all and I don't want to sour your new impression by bringing up memories of fully darkening cells or anything. But with an open mind searching for loops, I'm sure you'll love the new twist. It is a style I call "Rubber Bands."
Rules: Stretch some rubber bands over the posts in the grid, reaching vertically or horizontally only between posts. Each rubber band will surround exactly one given number, and each number in the grid will be surrounded by exactly one rubber band. The number indicates how many unit cells that rubber band surrounds. Rubber bands can touch at a post, but cannot share an edge and cannot overlap to both contain any square. Rubber bands cannot cross themselves. All internal (black) posts must either touch a rubber band or be inside a rubber band. Cells outside the rubber bands must form a single contiguous group.
I find it particularly challenging to solve Rubber Bands by just drawing the edges, but I also find particularly challenging puzzles to be very fun. So I hope you give this new style a try and solve it as the instructions intend. The new "internal post" rule is so much better than that 2x2 shaded square nonsense anyway. At least if you are being loopy.