The chemistry of what you are doing is extremely important, Mike. People use bleach (an alkaline) to clean mildew and break oils. Mixed with a surfactant, bleach can be used as a cleaner on several surfaces. There has been an ongoing debate for decades about the wisdom of using bleach. Bleach, if too strong, breaks down the wood. In fact, that is one of the ways paper is made - wood pulp broken down by a bleach mixture.
The reason many experienced professionals advise against the use of bleach is that there is a tendency to use it way too strong. You know - if three "glugs" are good, then four glugs must be better.
I think PWNA took the position years ago that bleach is fine to use in the hands of experienced professionals but can be abused by those who don't understand. I suggest that bleach (with an added surfactant) can be safely used at concentrations of 1% - 2% on wood.
Brightener, on the other hand, is an acid. It is effective at driving natural tannins back down into the wood. On cedar you can see the effect immediately while PT often doesn't show the effect for several minutes. Brightener is the secret weapon of the most successful contractors because it makes the wood as light and bright as possible. A semi-transparent sealer then looks so much better on the wood. Think about dying a white T-shirt and dying a dirty T-shirt. Which one will look better?
Applying the brightener neutralizes the caustic cleaner that was used (whether bleach or sodium hydroxide). It leaves the wood with an acidic surface, which oil sealers bond best to.
The steps to use are: 1) wash the deck with a good wood cleaner (either a stripper, a bleach/soap mix, or a percarbonate cleaner. 2) Brighten the wood immediately after washing it. Rinsing the brightener of is recommended but usually not necessary. 3) Allow the wood to dry and then apply the sealer of choice.
The "unknown chems" you refer to are likely sodium hydroxide based strippers. These caustic cleaners strip off any previous oil sealers. The contractor then follows up with a brightener.
You have a lot to discover as you learn about wood restoration. It isn't that tough, but you do need a working knowledge of the chemistry involved. You can search the BBS for previous posts and learn a lot. You might also consider taking a class. The difference, with the right knowledge, is faster jobs and higher customer satisfaction. This is not a trade you should learn by experimenting on your customers.