I thought bleach was just sodium hypochlorite???

As described in this post, Clorox Regular bleach is 6% sodium hypochlorite (chlorine), 4.7% sodium chloride salt, about 0.06% excess lye (sodium hydroxide), and a very small amount of sodium polyacrylate. All bleach and chlorinating liquid will have this ratio of sodium hypochlorite to sodium chloride due to the chemistry of the manufacturing process where chlorine gas is added to a solution of sodium hydroxide. The carbonate comes from carbon dioxide in the air.

The only difference between the two bleaches you listed is the small amount of sodium polyacrylate in the Clorox Bleach. It is added primarily as a metal sequestrant of iron and manganese to prevent them from reacting with bleach and yellowing clothes. Since the normal dosage for Clorox bleach is 3/4 cup and a normal wash load is 40 gallons over multiple rinses (so say 20 gallons for the water used with bleach), then that is a 1:427 dilution or around 1400 ppm FC. In pools, the dilution is at least 100 times greater so the effect of the sodium polyacrylate is negligible though it will build up slowly over time possibly sequestering some metal.
 
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