I assume your house is on a slab from the description. Therefore your subfloor is concrete and nothing will change that. Anything you put over the concrete before the finished floor will be referred to as "underlayment". When we talk about nailing a subfloor down, that referrs to a "built floor" on joists, over a crawlspace or basement. If you have a second floor, it is constructed this way. 3/4" to 1-1/4" tounge and groove plywood is nailed and glued to joists to produce a flat quiet floor that is very flexible in how it can be finished.
Slab subfloors are often finished directly with no underlayments. Padding and carpet are frequently applied directly on concrete as is a lot of vinyl. There are ways to add underlayment, but perhaps you could clarify what kind of project you have in mind.