I think at the basic level it is a developer who can handle both front end and back end tasks equally well. As a full stack developer gains experience then I think they start layering on other skills and abilities and in the end an experienced full stack developer becomes a jack of all trades, able to take on pretty much any dev task required. I think for a company looking to hire someone it will depend on their needs and budget. A big dev house likely needs more specialised people while a company just looking for a dev or two to run their website would likely need full stack developers who can do anything.
I personally consider myself a back end developer but if the need arises I am able to take on tasks across the whole spectrum of dev. This is because I work for a small company-start up (we are slowly losing our start up status and becoming a full fledged company).
I also think you will find full stack developers who started as either front end or back end developers and then added skills. Each of these will bring slightly different things and perspectives on how to do things.
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