Years ago, everyone working in tech was an IT generalist. They did everything (DB design, systems, applications, algorithms, code, networking, etc.). Today, the field has matured and people are able to specialize.
Sometimes, when old IT generalists work with new IT specialists, these sort of misunderstandings occur.
Years before everyone was apparently a generalist, you would have a separate DBA, a separate architect, sometimes even separate teams for implementing algorithms, etc. The mythical man month has a very nice section on splitting up the work over the various teams and that's a book written in the early 70s.
I think the actual boundary lies more in big vs small companies: small companies do not have the resources to hire specialists for every little subproblem, while big companies typically have enough employees that specialisation becomes a possibility.
I'm not sure. I take full-stack to mean the front-end, middleware and back-end of a webapp. I would still call it being a "generalist" when applying the concept to computer technology in general. For example, the CTO of an org should be a technology generalist, not a full-stack web dev.
Of course, this is just my personal opinion based on what I have experienced over the last 40 years.
Sometimes, when old IT generalists work with new IT specialists, these sort of misunderstandings occur.