Laundry bleach (regular unscented or ultra unscented) uses Sodium Hypochlorite as the active ingredient, either 5.25% or 6%. The rest is "inert" ingredients--basically salt water.

If you go to the pool store and buy "liquid chlorine" in either gallon jugs or blue carboys you will be getting the same thing: Sodium Hypochlorite solution. Sometimes it will be 6% (exactly the same as Ultra bleach) or 10% or 12.5% (which is really 10% because it breaks down SO quickly).

Sometimes they call it "Liquid Shock" when it's 12.5%.

But the bottom line is that it is EXACTLY the same stuff as laundry bleach with a different label, and maybe a stronger concentration. Caveat: Pool store guys will tell you if you use liquid chlorine you MUST add muriatic acid to compensate. Do NOT believe them. Test your pH and add acid only if pH is high. You rarely will using bleach/liquid chlorine.

Dry pool store chlorine can not only be calcium based (Cal-hypo), it can also be di-chlor or tri-chlor. Cal-hypo adds calcium-which concrete pool owners need (up to a limit--400ppm), but vinyl pool owners don't (although pool store guys will swear on their saintly mother's head that you do--they are either honestly wrong or lying).

Di-Chlor and Tri-Chlor both add stabilizer--Cyanuric Acid or CYA. You need some but too much is a BIG problem. They are also extremely acidic and will lower your pH--whether you want them to or not.

Finally there's a lithium chlorine powder. It costs a fortune, has very little active chlorine and may have unexpected effects--I don't know what concentrations of lithium do in water.

Bottom line: Most of us use laundry bleach to chlorinate. I do.