The flux capacitor first appeared in the movie "Back To The Future"; it's the gizmo that makes time travel possible, according to Doc Brown.
The entire "Back To The Future" concept exists in Toobworld, Skitlandia, and the Tooniverse. Concentrating on Earth Prime-Time, Doc Brown proved to be a serlinguist at the beginning of the cartoon series:
And here's a 25th anniversary blipvert update to "Back To The Future" which should fully absorb the movie trilogy into the TV Universe:
But it also exists as an actual movie, which then must be a fictionalized version of the "true" events in Toobworld (even though the movie came first in our own timeline).
This is why TV shows like 'Stargate: SG-1', 'Stargate: Atlantis', '10 Things I Hate About You', and 'The Thick Of It' can refer to "Back To The Future" as a movie, while shows like 'Star Trek: Deep Space Nine' and 'Malcolm In The Middle' can refer to the flux capacitor as if it really existed.
The appearance of the sketched-out flux capacitor on 'Community' would straddle both ideas.
(A very big thanks to Sean for bringing it to my attention and for supplying the picture!)