"Full stack" is just a re-fusion of the "front-end" and "back-end" web developer separation that was already tired. Something about "the geeks" not having aesthetic sense and "the backend" being too "hard" for "the designers".
In short, full-stack developers just "get it": network, database, ui-design, system calls, OS configuration, software construction, front-end, back-end, etc. There are trade offs everywhere: risk, complexity, effort, cost. Usually solving improving conditions for one area of the system just push these trade offs to other areas. Full-stack developers get this and can help make better architectural and implementation decisions.
My main point was that the separation into these buckets is strained already.
Good, well-rounded developers should know the full ecosystem they're operating in. Some will always be better at and more interested in something, other in other things, that's no surprise, but we don't need to invent a stream of vague titles.