There's an anecdote about the production of Star Trek IV
that perfectly illustrates this background actor/extra vs. day player distinction.
From the Memory Alpha article on ST4:
In an interview with StarTrek.com about the scene with Koenig and Nichols asking about the location of the naval base, Layla Sarakalo stated that she approached the assistant director about appearing with the other extras and was told not to answer Koenig's and Nichols' questions. To the annoyance of the other extras, she did answer them and had to be inducted into the Screen Actors' Guild as a result, as the production crew found the line too amusing to be cut out.