Bleach is just the common name for sodium hypochlorite. "Liquid chlorine" sold by pool stores is usually just slightly higher concentrations of sodium hypochlorite.

All forms of pool chlorine add chlorine to the pool + something else:

1. Sodium hypochlorite adds chlorine plus some salt.
2. Calcium hypochlorite adds chlorine + calcium + some alkalinity
3. Trichloro-s-triazinetrione (one of many 'official' names for trichlor) adds chlorine + stabilizer + acidity
4. Sodium dichloro-isocyanurate (one of many 'official' names for dichlor adds chlorine + stabilizer + some acidity.

Bleach is a liquid; cal hypo is almost always a white granular material that is slow to dissolve; trichlor is usually formed as 3" pucks; dichlor is a fast dissolving white granular material.

The easiest method of starting off with an Intex pool is here:
Super-simple-pool-chemistry-recipe-for-Intex-type-pools-start-up-amp-routine-care.

You don't have to understand much of anything, to follow those instructions, but after you follow them for awhile, things will begin to 'make sense'.