Fossil means "dug up". So both fossil remains (remnents of ancient plants and animals) and fossil fuels are called that because they are dug (or drilled) from the ground. As opposed to harvested fuels (wood, dung, etc.).
https://www.etymonline.com/word/fossil
The popular meaning of "fossil" has somewhat orbited around the usage such that we associate "fossil fuels" with "fossil remains" rather than "dug from the ground".
I don't know if that makes helium a "fossil" resource, though I could see the argument for that. We don't refer to other minerals (e.g., iron, much of which comes from banded iron formations, or limestone, from seashells), as "fossil" resources, despite both being dug from the earth and biological in origin.
There was a movie named Moon about a decade back where that was the main character's job, helium mining on the Moon.
That's not to say it would be easy, but it's closer than the Sun. Because it is everywhere.
In the various Star Trek shows, ships are made with something called "Bussard collectors" which basically scoop up particles like helium and hydrogen from space for use in the ship.
Obviously both of those example are fiction. We don't have the capability to mine on the Moon or catch elements free floating in space. But those fictions are based on the fact that those elements are that abundant.
I think I read somewhere that despite this being a science fiction trope forever, there may not be a region between "too thin to produce net power" and "thick enough to blow up a spaceship at relativistic speeds". And in practice, the interstellar medium turned out to be the former, too thin.
In fact, I'm not sure but what someone may have calculated drag would exceed power generated, regardless of density.
It is renewed, by radioactive decay within the Earth, but very, very slowly.