Collagen vs Gelatin

The core fact: they're the same protein, different states. Gelatin is collagen that's been partially hydrolyzed (broken down) by heat — it's what you get when you simmer bones, skin, and connective tissue long enough that the collagen unwinds and becomes soluble. Cool it down and it sets into a gel (this is why bone broth gels in the fridge, and why Jell-O is gelatin).

Collagen (hydrolyzed/peptides) goes a step further — enzymes break gelatin down into smaller peptide chains, which is why collagen powder dissolves in cold liquid and doesn't gel, unlike gelatin.