I don't think it's as hard and fast as never buying a "pool" label, just that it's worth comparing products that are available for other uses (like liquid chlorine, muriatic acid, baking soda, etc). Cyanuric Acid, for example, is probably not easily found other than as a "pool" chemical (aka Stabilizer).
I'd double check what you were looking at in the pool aisle; the sizes and concentration don't sound normal. Do you have a picture? I'm looking at Walmart's website (which isn't always accurate as to what's in the store). When I search near Tucson, they have the 2-pack (i.e. 256 oz total) of 10.0% concentration for $10.54, which is going to be quite a bit less normalized against the cleaning aisle one.
Also beware that cleaning bleach often has additives these days that you don't want, and sometimes they're not well disclosed. Clorox in particular used to be good "plain" bleach, but I believe most/all of their products have "Cloromax" and other stuff in them now.