Naptha, Stodard's solvent, white spirits, mineral turpentine and odorless mineral spirits are all forms of mineral spirits. They come in a wide range of distillation fractions and purity levels from heavy to light. If you don't believe it, compare the CAS numbers in the MSDS sheets. Or simply look at the
Wikipedia entry for white spirits, which seems to be accurate. Odorless spirits start as regular mineral spirits and the shorter hydrocarbons are removed. They're the ones that evaporate to become airborne more easily and are inhaled to provide an odor. They also can help attack some things faster as a solvent, so there is some degree of trade-off here.
Acetone vapors are known to cause CNS damage over time if you are exposed to them too much. MEK is worse. TCE was even worse, when you could still get it. When I was young and latex paints were uncommon, the fact house and wall painters started having nervous system problems as they aged was common knowledge, and that would mostly have been from mineral spirits and turpentine. So enough exposure to about anything can get to you. I just don't think most of us are at risk to get that much exposure from cleaning guns unless we do it professionally.
Acetone helps Ed's Red penetrate fouling as well as softening shotgun wad LDPE. If you are not cleaning shotguns, you can replace a quarter to half the mineral spirits with Kroil to speed up penetration, but it's no longer as inexpensive doing that. You can add and ounce of tea nut oil or wintergreen oil to the same effect, but, again, it adds cost.
I've left field stripped 1911 parts sitting in Ed's Red for up to a couple of weeks, and the caked-on fouling gradually turns to a sort of sludge that flows toward the bottom of the container over time. In a rimfire, the best effect will be had from plugging the bore and filling it and letting it sit for a day or more before patching it out. Enough penetration will sometimes let you patch out metal fouling mechanically. It can just break loose and come out on the patch. For that reason, if you clean with Kroil, giving it time to work makes a difference.