"Full-stack" web developer does get thrown around. However I believe that is still has a pretty static definition.
My understanding is it is a "jack of all trades" scenario. Except by "jack" I mean ver knowledgable just not a master, and by "all trades" I mean the layers of of a full stack developer mentioned here:
I would like to think that I am on my path to becoming a full stack developer. I believe this takes a long time. So I started by taking freelance work that enabled me to get my hands dirty. The more client need I answer the more I become familiar with all of these layers.
The only path I know to becoming a full stack developer is just start building things.
Want a starting point? Build an SPA that communicates with Wordpress for managing the state over the new WP JSON REST API, using Backbone.,js.