I like this post from Chris Coyier. This quote in particular.
A full-stack developer on that stack means you know Linux, Apache, MySQL, and PHP. (Abstractly: server software, web server, database, back-end language.) This site runs on that stack, and I'm solely responsible for its development, so I guess I'm a full-stack developer in some loose sense.
But "loose" is a generous interpretation. I don't know the first thing about Linux, except that's what runs my web servers. I don't know much about Apache, except that I sometimes use HTAccess directives to do things. I could count the number of MySQL queries I've written on my two hands, and I only really know PHP in the context of WordPress.
I don’t think that most places looking for “full-stack” developers or people saying they’re “full-stack” have a solid definition to go with it. Most companies use the term so they can hire a single person that can maintain anything. No specialization needed, just do it all and do it well or you’re not “full-stack”.