Liquid chlorine and bleach are the same thing, the only difference is concentration. Liquid chlorine sold in the pool store or hardware store is typically 10% sodium hypochlorite while laundry bleach, as of late, is 6% sodium hypochlorite. If you use laundry bleach then you need to make sure it’s not the scented or splash-less variety and that it doesn’t say “fabric protection technology” (or Cloromax Technology) on it.
Use pool math to figure out how much you need to add to your pool. Pools typically need 2-4ppm FC per day to make up for UV loss and bather load.