We web devs actually have pretty solid definitions for "front-end," "back-end," and "full-stack." The back end deals with work on the server done after an incoming HTTP request comes in and involves preparing the HTTP response, including preparing the outgoing data for the templating layer if applicable (eg, when doing web page responses rather than JSON, XML, or binary responses). The front end deals with building templates such that that data becomes a standard web page, using CSS to style that page, and using JavaScript to implement client-side interactivity. A full-stack developer will be constantly switching between work from both sides of this divide rather than primarily focusing on one or the other.
If a job listing for a front-end developer is expecting applicants to know PHP beyond a "writing templates" level, it's either a poorly-written job listing or its creator has unrealistic expectations of its applicants - sadly, neither case is very uncommon in this industry.
At any rate, someone calling themselves a full-stack developer isn't implying they can do embedded, as that sort of stuff is pretty far afield of web development.
If a job listing for a front-end developer is expecting applicants to know PHP beyond a "writing templates" level, it's either a poorly-written job listing or its creator has unrealistic expectations of its applicants - sadly, neither case is very uncommon in this industry.
At any rate, someone calling themselves a full-stack developer isn't implying they can do embedded, as that sort of stuff is pretty far afield of web development.