So, we can almost all agree that graphic design is broad and can encompass many fields such as logo design, web design, illustrations and even photography.

Design utilizes many things, but illustration and photography are different disciplines, while logo design, web design are under the umbrella of graphic design. A designer may be adept at illustration or photography to utilize those skills in their work, but those are still different disciplines, the same way painting, sculpture, etc would be.

That aside, really you can let the work dictate what you do. If you go get a job at a studio/company where you're working on books or magazines, you'd be an editorial designer. If you go somewhere else and do packaging, you'd be a packaging designer. And so on. Usually such titles don't really matter anyway, because your portfolio will show your abilities.

In terms of freelancing, where the focus or requirements of a given job/client could vary from one to the next, it isn't relevant to give yourself such a title, graphic designer is fine, where you'd just make sure your marketing properly communicates your skills or desired areas. If you want to do logos/branding, you wouldn't have a website with zero logos/branding and only editorial layouts, for example.

In general, as long as your design foundation, your core skills and understanding are sound, you should be able to go into whatever area you want, it just becomes about growing the experience within certain areas to overall become better. If you did logo/branding for 5-10 years then tried to do editorial, you might not be as good as someone doing editorial for 5-10 years, but you're not going to be a layman. You'd still have an understanding of design process and fundamentals, it'd just be about learning the specifics of that new area.