Actually, switching a retainer to DoH won't work at all. The DoH (crafting) classes aren't available to retainers.

Switching to a DoL (gathering) class will, though. Is that what you meant?

I definitely understand why the wording in the second screenshot could be confusing. There's still a distinction between what is a job and what is a class even if players tend to use them interchangeably at times. It's a difference that players would love to see SE remove but at this point, it's too firmly entrenched in the game coding.