In it's natural state, chlorine is a gas. Many large commercial pools actually use gas injection systems to chlorinate their pools.Interesting read on the chlorine. Do most of you use liquid bleach? I was about to buy an $80 bucket of tabs.
Now, to change chlorine into something we can use at home it needs to be bound to something to turn it into a solid. The "somethings" that are commonly used are stabilizer (also known as CYA), calcium, lithium, or --- get this water.
All of these add a little salt to your water, but they add something else.
Cal-Hypo add calcium
Tri-Chlor and Di-Chlor (tabs and most granules) add stabilizer
Lithium hypochlorite adds lithium
Liquid chlorine adds - water
Notice I said, liquid chlorine. It is available in multiple "forms", all of them are just different percentages of chlorine in the solution. We generally call anything below 8.5% "bleach" and there are other percentages up to 12%
I guess this was my long winded way of saying, use whatever liquid chlorine is most economical in your area. That may be bleach, but higher percentages sold by pool stores may work out better dollar wise.