The short answer would be that you your primary logo(type) is for ideal situations in which you can use it the way it has been designed in terms of size, color, position, (print) quality, (print) medium and quite possibly even lighting, while your secondary logo(type/s) are for any other variation of the ideal set of circumstances required by the primary one to be displayed properly.
The long answer is that rarely one logo fits and suits all situations and that designers should be aware of that just as much as their customers should be, while at the same time a designer designs for his or her customer's customers in mind.
In using the example of the bearded man, a designer's customer (the company using this logo) might not see a problem with using this one single logo for everything, from their website, to colophon, stamps, invoices, all regardless of size changes, quality changes and any other combination of every change imaginable, depending on which "product" is being branded with a/the logo.
The bearded beau's facial outline could possibly disappear if simply shrunk down to fit on an invoice template, so making it thicker helps with keeping that part of the logo's identity (it's supposed to look like a bearded man with a hair-do and not like Bigfoot, for example) and keeping brand recognition without sacrificing style or identity.
I personally find myself often referencing sources like 50 Meticulous Style Guides Every Startup Should See Before Launching on "Design School" for both inspiration and examples.
I hope this helps.