We're getting closer!
How about this:
Embroidery (thought I'd add it to the discussion as it's related and the tag already exists anyway):
The art of decorating various materials with ornamental designs, often raised, made of fabrics through the use of needle and thread.
Can also include small items like strips, beads, etc.
Embroideries may be "sewed over", or worked through the underlying fabric.
A form of trim when applied to clothing.
I'm not sure if there's much use (or worth to the confusion) to separating this from trim as far as danbooru goes. Unless we want to use it as the equivalent of trim for non-clothing, or only tag obvious, isolated designs.
Lace:
A type of fabric/cloth made with an abundance of noticeable open space between threads.
It usually looks like fine netting with many intricate patterns and differing density. It is not limited to clothing.
It can be added as a trim, or entire clothing pieces (often underwear) can be made of it.
Should be seen as a material for tagging purposes.
Pleat:
A type of gathering. It basically seems to vary only in how it is made. For danbooru purposes however, it is considered as the visual distinction of the folds in gathers being pressed, so you get a sharp crease.
Gathers:
Quite literally "gathering" large amounts of fabric, in a smaller space so that it creates many creases or "loops".
Related to but not be confused for ruffles.
Trim:
Any decorative "extensions" applied to cloth.
Not limited to ruffles.
Edging:
It is basically a trim on the edge of clothing. It can refer to some non-trims as well. Personally I don't think it should be differentiated unless we want to use it for things like the pink border in post #982428, the black borders in post #972872, or the red "dotted" line in post #974782, and not consider half of these trim.
Frills:
When a strip of fabric is gathered at one side, leaving the other free, and then applied to clothing as a trim, or is used as such. Compare to gathering, which is a more integral part of the base clothing layer.
The two can be hard to distinguish at times.
It is a form of trim.
Ruffle:
Alias to frill.
Fringe:
An ornamental border of threads left loose or formed into tassels or twists, as often seen in Native or South American and typical "far west" clothing.
It is a form of trim.
Short summary of proposed changes (outdated):
While at it:
Examples (some may be NSFW):
post #999466: Underwear made of lace.
post #972719: Her dress is gathered. Her thighhighs have a trim made of lace
post #971335: Lace-embroidered garters. The white garters on the right have what looks like a lace trim as well. The black garters on the left, and the white thighhighs on the right have a gathered trim, aka ruffle/frill.
post #972872: Black lace trim
post #915736: Gathered, but quite ambiguous.
post #969748: Ruffles everywhere. The large blue cloth around her does not qualify for "gathered", it is a physics effect. (just saying)
post #973540: Her bra has a lace trim, and lace embroidered on it (which is also a trim of course, of the embroidered type).
post #972899: Many lace parts. Perhaps some trim too, unsure.
post #974782: Lace trim I would assume. (example of tatting, too)
post #996832: Ruffles.
post #978708: Gathered.
post #957699: I'd consider the apron to have ruffles and the sleeves gathered, though they could be considered frills too. The white dress under the black one seems gathered but could fall under the "gathers used as frills" clause, and has a ruffle over her chest. The black dress also has ruffles over the chest (at least I think that's what it's supposed to be), and the thing with the blue line around her neck is just trimmed.
post #996492: Gathered/pleated skirt.
post #948794 and post #945118: More obvious examples of danbooru's use of pleat/pleated.
Note: post edited to address the points mentioned further down.