No, the chlorine is made by electrolysis of brine in what is known as the chlor-alkali process that produces chlorine gas and sodium hydroxide (lye) in two separate chambers separated by a membrane. The lye is removed and purified and added to very clean water free of metals and the chlorine gas is then bubbled into it. The result is sodium hypochlorite which we know as chlorinating liquid or bleach. This is shipped to the pool store, often as 15% strength, and fills tanks, carboys, or gallon jugs.
For sure, the chlorinating liquid or bleach is not made from any powder. There is no powdered sodium hypochorite. All solid forms of chlorine would produce something else, either lithium hypochlorite, calcium hypochlorite, or chlorine with cyanuric acid (from Dichlor or Trichlor).