Earlier quoted context omitted.
About a week ago it occurred to me that "Full Stack Developer" is what we used to call "Software Engineer." It's like suddenly understanding some idiom the locals are using; everything in the universe made a lot more sense.
Is that true? I always took "Full Stack Developer" to mean "We're too cheap to hire a proper ops team, so we're going to expect you to serve triple-duty as Sysadmin, DBA, and Software Developer." Maybe I've been unfairly ignoring a lot of postings?
If that's your impression, then I think you have been. By full-stack developer, many people in the start-up world simply mean someone who can work at all levels of web development, from server-side programming to Javascript, CSS, and HTML.
It's not an unreasonable use of the word, since web developers have long talked of "their stack", meaning what they use for server-side framework, caching, http server, as well as client-side frameworks and development environments.
I don't think most people use the term to include sysops, although in a small start-up you will inevitably be doing a lot of that.