There's a sad lack of rigor in the use of terminology in the shooting sports, and especially when it comes to the differences between "factory," "remanufactured," and "reloaded" ammunition. Here's how I break it down:
"Factory" ammunition is all new manufactured ammo, using brand new cases.
"Remanufactured" ammunition is all new except for the cases which are once fired. Remanufactured implies that a large and properly insured company is doing the remanufacturing, using well designed processes and very well selected loads. It also implies scrupulous quality assurance.
"Reloaded" is what I do on my bench. I select the loads, and I use either new, once fired, or "more than once" fired cases, depending on the load. I'm the only one shooting this stuff, so I don't need insurance against my own potential carelessness, and I'm my own QC department (but since I did that job professionally for several years in a different industry, I think I do a pretty good job of it).
With all that said, I would not hesitate to use ammo from a well-known remanufacturer like Black Hills. There are a number of smaller firms that make well reputed remanufactured ammunition, with a few others that make stuff that may or may not be great. Go with the reputation of the remanufacturer, but do plenty of research first.