First, please remember that, though the definitions I gave you are generally valid, people in the pool business do not always use those words that way. The pool industry is not filled with folks with BS degrees in chemistry or chemical engineering. Generally speaking the long time PoolForum users, who are just pool owners, know more about pool chemistry than most people in the pool industry.

The problem with all three of those words is that they do NOT tell you what the speaker (or writer) had in mind when he/she used the word. Often, it turns out that what they meant was something really vague and unspecific.

So, those words are often not really useful in actually communicating a specific meaning.

Certain statements do have generally consistent meanings. For example, "I'm gonna go shock that pool" USUALLY means, "I'm gonna go dump a bunch of chlorine in that pool".

There's another issue embedded in your questions: all forms of chlorine add chlorine (HOCl / -OCl) plus something else to the pool (salt, calcium, stabilizer, whatnot). It's the chlorine that oxidizes, regardless of what ELSE is present in that form of chlorine.

But, there's another terminology issue here: "chlorine" can mean the element, Cl2 - chlorine gas. Or, it can mean 'pool chlorine' IN WATER, that is HOCl (hypochlorous acid) + -OCl (hypochlorite ion). Or, it can mean pool chlorine in a container: calcium hypochlorite, sodium hypochlorite (bleach), triclor (usually, tabs), diclor (sodium dichloro-isocyanurate -- usually granules) or another compound. Or, it can mean various disinfection by-products, as in "The pool smelled like chlorine", which usually means, it did NOT smell like chlorine gas, HTH, bleach, triclor or another compound, but DID smell like nitrogen trichloride, chlorurea, or another byproduct from the chlorination of 'goo'!

I will assume then that the numerous pool shock products have nothing to do with achieving breakpoint chlorination, but they are used as some sort of magic tonic?
Well, sorta, but not really. The pool shock products don't produce breakpoint chlorination, not because they don't contain chlorine (tho they sometimes don't) but because "breakpoint" does NOT occur with ordinary pool "chloramines".

If you produce chloramines by mixing chlorine and ammonia in your pool (NOT in a container, PLEASE!), then you can chlorinate THOSE chloramines to breakpoint. This happens when you use "Yellow Out" or other ammonia based algae treatments. BUT, if you produce chloramines the normal way, by mixing chlorine with 'people goo', breakpoint will NOT occur, because those compounds (chlor-urea, et. al.) don't react that way.

By the way, chloramine DOES have a specific and consistent meaning: it refers to compounds -- usually nitrogen containing -- that occur when you chlorinate water with waste products OR ammonia in it.