Gelatin
Classically, gelatin is hydrolysed collagen, where collagen is the protein from bone of mammals.
Gelatin is used mostly as a thickening agent, e.g. in gelatin puddings.
It's used in a bunch of soft candy, from marshmellow to gummy things to liquorice.
It's also one way of clearing wines.
Kosher and/or halal gelatin - observes the respective rules.
In practice is often fish based, sometimes seaweed based, but may still be animal.
Vegan gelatin might be agar agar/carrageenan (based on seeweed), cornstarch, pectin, xanthan gum, or one of a few others, possibly moving on to thickening agents in general. Which one of these is preferable depends on the properties you want ().
Whether these can be labeled gelatin depends on recognizability marketing, food regulation laws, and personal pedantry.
Note also that the ingredients list is often more informative than the product name (also due to potential allergens).
See also: