Exactly. In this case both chains require first cause but in general first type of chain requires first cause by necessity while the other type of chain could in principle be with or without first cause (endless regression).
The illumination example could, in principle, be the result of light reflecting forever off of various things, with the last reflection being off of the moon. Or, it could, in principle, be that light has always been moving and only reflected off the moon to illuminate the room. So 'original source' of light would be required.
So either could *in principle* be the result of an infinite regress. And either could *in principle* be the result of a first cause.
That's why...
Aquinas was interested not in a beginning cause but in a sustaining cause, for he believed that the universe could be eternal—although he believed on the basis of revelation that it was not eternal. He constructed his cosmological arguments around the question of what sustains things in the universe in their existence. (Stanford Encyclopedia of Philosophy)
And why would a 'sustaining cause' be required at all? For that matter, why could not physical reality be that sustaining cause?
And, again, given the lack of *necessary* sustaining causes, why would we think any exist at all?