I'm not sure right now whether this will arrive at an actual answer, or just ramble through some musings & definitions… but if I can't shed at least a little light on an industry I actually work in, then I'll hang up my hat ;-))
US uses 'season' for 'one year of a show's life', UK unfortunately uses series for both a single 'year' & also the entirety of the show's life, though this is changing & the UK is adopting the term season in recent years, so I'll use the US definition to distinguish.
Several episodes making up a whole Season - consisting of either one long plot, several independent stories containing roughly the same characters, or even several completely independent stories. A documentary series would be a good example of this last form.
Even soaps have seasons - even if they broadcast 52 weeks of the year, but they are rarely advertised to the public as such.
Specifically, one long plot (or plot arc, which can be broken into sub arcs, to add excitement at episodes throughout the series rather than trying to save it all for the last episode); even if that plot digresses & has episodes that don't appear to form part of the whole. Doctor Who may be an example of this, where each story stands reasonably well alone, yet there is always some underlying long-plot usually only slowly revealed until the season finale.
A term that can really only be applied if the previous incarnation, be it movie, single-episode or short-season drama, would appear to be final & complete at the time it finished; or alternatively, usually from an existing series of books etc., the term would apply, as nominally each book would be self-contained to an extent. Otherwise it is simply 'season 2'. To make it more confusing… Harry Potter has sequels, Game of Thrones does not. Star Wars has sequels & prequels.
… and finally… an answer… almost
If each episode is not part of an overall plot arc, or if the overall arc is not needed to watch any random episode without becoming lost as to what is happening, that show would simply be termed episodic. The Simpsons would be a good example.
I don't know of any single term that would describe 'one independent episode' as the OP asked; which is why we end up having to dodge & squirm, using 'episode', stand-alone' etc to try describe it.
NB - episodic can also be used to describe a show that is written to be a long plot, yet the makers concentrated more on the individual plot of each episode at the expense of the long plot. Such use is slightly derogatory.