Welcome to the forum from sunny and too-warm Arizona!
Now for your question. Probably 25 years ago, the major US ammo manufacturers met the challenge of low-cost imported ammo by coming out with their 'generic', plain-boxed ammo lines in popular calibers. I'm guessing Winchester led the pack as their "Winchester White Box" (WWB in gun-forum speak) is the most ubiquitous. Remington followed with UMC as did Federal with their American Eagle brand. Interestingly, Winchester was the only one who kept their name on their economy line. Remington had long ago ditched the Peters brand but resurrected the UMC label (for Union Metallic Cartridge, a company they acquired eons ago), and Federal invented the AE name.
So what's different about the generics? The answer is anything from "very little' to "a lot." As far as exterior ballistics are concerned, the generics match the high-priced spread identically - at least in the catalog. But if you ever looked at a handloading manual, you know that there are any number of 'recipes' that can launch a given projectile at a certain velocity. So while the generic-label bullet may leave the gun at the same speed as the full-priced ammo (which I'll call 'regular' from here on out), there may be a lot of other things goin on that are less obvious. Typically, the generic stuff is dirtier and leaves more residue at both chamber and muzzle ends of the gun than the regular ammo. Muzzle flash will almost always be greater, especially when compared to defensive ammo which uses powder formulated to minimize flash. And overall quality won't be as good. I've seen blind primer pockets, upside-down primers, primers not seated flush, crooked bullets and cases with crushed case mouths come out of boxes of generic ammo. Accuracy is typically another victim to the lower cost. In particular, the UMC brand has never shot well (accurately) in any of my handguns compared to comparable loads from Win and American Eagle.
With respect to brass, in a couple of years of reloading, I have yet to notice a difference in brass between generic and regular. I don't know about the bullets, but my engineering sense suggests that there may be some relaxed quality for the bullets used in generic, like greater tolerances on bullet weight or concentricity. The ammo makers won't sell anything that doesn't meet SAAMI specs so it's safe to use, but greater variability leads to reduced accuracy for sure.
I've been around the shooting sports a long time but I never heard it was bad form to ask what the difference was between generic and regular ammo lines. Heck, you're a consumer and you deserve to know what you give up to save a few bucks. Ask away, but just don't expect you'll get the definitive answer.
So your question boils down to "which do I use?" One consideration is that you won't find a huge selection of defensive bullets in the generic brands, although there are a few JHP loadings, so that may drive you in one direction. If generic ammo was all I had available to me, that's what I would use. But since there is better stuff available for defense, the common approach is to use the plain box stuff for practice, and load up with "designer" ammo for carry and home defense.
