In the midst of writing this, I see Dr. Rocket has made a distinction here, and he is likely right. I had written the following, which is apparently more about general usage as opposed to technical usage....
Originally Posted by Roobydo
I could be wrong, but I think 'space' is generally just shorthand for spacetime. With a finite speed of light, space (in astronomical terms) necessarily involves this time delay between what you are observing and when it actually happened.
But as loglo's point implies, current understanding of the 'spatial medium' is apparently so free of fundamental observations, not much can really be said or claimed about it. So meanwhile, space is simply coordinatized to match observations. The more distant an object, the more is its distance increasing. (Well, technically, there is some variation there. Early on, expansion was slowing, then constant, now accelerating.)
At any rate, does that say anything about the space between here and there? Is it 'stretching' or 'reproducing', or is there any 'materiality' to space at all? Since independent observations confirm spacetime is very close to flat, modern scientists have pinned ~70% of the entire mass of the universe as coming from... 'empty' space. So there's apparently some materiality there, but what that materiality is, is rather up in the air, so to speak, especially with respect to how it can cause the expansion to accelerate.