A gelling agent is any ingredient that causes a liquid to set into a semi-solid, structured gel — think of how a liquid jelly mix firms up into something you can slice or hold its shape. A vegan gelling agent does this same job using a plant, algae, or microbial fermentation source instead of animal collagen.
It's worth separating two words that get used almost interchangeably but aren't quite the same thing: gelling and thickening. A gelling agent creates a structured, often sliceable or moldable set — a jelly holds its shape when turned out of a mold. A thickener increases a liquid's viscosity without necessarily creating that same firm, structured set — a sauce becomes thicker, but it still pours and doesn't hold a shape on its own. Several ingredients on this list, like guar gum and xanthan gum, fall more into the thickening category than true gelling, which matters a lot when you're choosing one for a specific recipe.
Gelatin isn't vegan for a straightforward reason: it's extracted directly from animal collagen — the connective tissue, skin, and bones of cattle, pigs, or fish — through a boiling and purification process. There's no plant equivalent of collagen, which is exactly why "vegan gelatin" isn't a single ingredient but a category of unrelated substitutes.
Those substitutes behave differently from each other because they're structurally different substances entirely. Agar and carrageenan are both extracted from red seaweed but form gels through different mechanisms. Pectin comes from fruit and needs specific conditions — usually sugar and acid — to set at all. Gellan and xanthan gum are produced by entirely different fermentation processes using different bacterial strains. There's no reason to expect them to act alike, and they don't.