Inspired by the following:
I realized that my own answer to that question hinges on the idea of features having the same name, but the Fire Elemental actually has two different features that cause extremely similar effects.
Notably it has the Fire Form trait and the Touch attack which state:
[...] In addition, the elemental can enter a hostile creature's space and stop there. The first time it enters a creature's space on a turn, that creature takes 5 (1d10) fire damage and catches fire; until someone takes an action to douse the fire, the creature takes 5 (1d10) fire damage at the start of each of its turns.
[...] If the target is a creature or a flammable object, it ignites. Until a creature takes an action to douse the fire, the target takes 5 (1d10) fire damage at the start of each of its turns.
Do these two ongoing effects stack with each other?