The bleaching agent in all commonly available bleach powders is hypochlorite. Calcium hypochlorite is a pure compound with the formula $\ce{Ca(OCl)2}$ and is the active component in most bleach powders. (Note: active does not necessarily mean the most abundant component).
You presented three examples of formulations for bleaching powder that you have encountered:
- $\ce{Ca(OCl)2}$
- $\ce{Ca(OCl)Cl}$
- $\ce{CaCl2 + Ca(OH)2 + H2O -> CaCl2\cdot Ca(OH)2\cdot H2O}$
The third species, $\ce{CaCl2\cdot Ca(OH)2\cdot H2O}$, cannot be a bleaching agent of any type because it does not contain hypochlorite. So I view that as plainly incorrect.
According to wikipedia,
Bleaching powder is made with slightly moist slaked lime. It is not a simple mixture of calcium hypochlorite, calcium chloride, and calcium hydroxide. Instead, it is a mixture consisting principally of calcium hypochlorite $\ce{Ca(OCl)2}$, dibasic calcium hypochlorite, $\ce{Ca3(OCl)2(OH)4}$, and dibasic calcium chloride, $\ce{Ca3Cl2(OH)4}$ [7].
I was able to find the source cited by Wikipedia online; it seems quite authoritative. It says:
Calcium hypochlorite solutions are made by suspending lime or hydrated lime in water and adding
chlorine. However, reacting lime with water generates lots of heat, and this heat must be allowed to
dissipate before chlorination. The maximum concentration is ∼85 g/L
of available chlorine, above
which dibasic calcium hypochlorite begins to precipitate.
Chlorination can be done in a batch or continuous reactor similar to those used to make sodium
hypochlorite, except that agitation is needed to maintain the suspension. In a batch reactor, agitation
can be achieved using a mechanical stirrer, or, more effi ciently, by circulation. A centrifugal
pump is used to pull the solution from the bottom of a conical tank and then reinject it tangentially
to create a strong vortex. Alternatively, the solution passes through a packed tower before it returns
to the tank. The packing in the tower creates shear that breaks the particles apart before the chlorine
is injected at the bottom of the tower.57 The reaction is as follows:
$\ce{2Cl2 + 2Ca(OH)2 → Ca(OCl)2 + CaCl2 + 2H2O}$
[...]
Hemibasic calcium hypochlorite, $\ce{Ca(OCl)2\cdot 0.5Ca(OH)2}$, can be precipitated from a solution of calcium hypochlorite at 40–80°C.143 These solutions are commercially made by chlorinating a
slurry of hydrated lime.5
The precipitate is removed by filtration and dried. Although it may still be
made in Asia, it has not been made in the United States or Germany since 1955.
[...]
Dibasic calcium hypochlorite, $\ce{Ca(OCl)2 · 2Ca(OH)2}$, is commonly used as an intermediate in making calcium hypochlorite, $\ce{Ca(OCl)2}$. It has never been successfully marketed as a product because it dissolves much too slowly.
[...]
Although calcium hypochlorite dihydrate, $\ce{Ca(OCl)2 · 2H2O}$, can be made by chlorinating a suspension
of lime, it is difficult to filter, partly due to the presence of calcium chloride. Calcium chloride also reduces the stability of the dry product. [...] Sodium hypochlorite is commonly added to convert calcium chloride to calcium hypochlorite
as follows: $\ce{CaCl2 + 2NaOCl → Ca(OCl)2 + 2NaCl}$
Pages and pages follow with detailed process descriptions for the manufacture of various formulations of bleaching powder. Suffice it to say, an ideal powder would be something like pure $\ce{Ca(OCl)2 · 2H2O}$, but this is very difficult to prepare economically, because of contamination with various amounts of chloride salts, hydroxide salts, or (depending on the route of manufacture) sodium salts.
