I've often seen the first episodes of the various Star Trek series referred to as pilot episodes. As I understand it, a pilot is an episode that is produced to see if a series is worth commissioning and if so whether any changes should be made to the series format, cast etc. This is what The Cage and Where No Man Has Gone Before were, but from what I've read, The Next Generation had already being given the go-ahead as a series before Encounter At Farpoint was filmed, and only a short gap before the next episode was filmed. Would it not be more correct to refer to it as the premier episode rather than the pilot? And the same for the three Trek shows that followed.
WIthin the television industry, technically yes. But as with much of colloquial language, actual popular usage in the real everyday world does not necessarily exactly follow the precise, technically correct definition as used by specialists in a particular field. So to the public, "pilot" is often a convenient shorthand way to refer to the first episode of a series. And it happens with lots of TV shiows, not just Trek. Kor
Discovery (as I understand it) was approved without a pilot, it simply went into production. The first episode won't be a pilot, just the first episode.
What Kor said. Decades ago it was more common to order a pilot for a potential series. Sometimes these aired, most times pilots never did (there's a ton of pilots that never aired; you can find a few on Youtube). Sometimes a pilot needed to be re-filed (maybe certain cast members weren't working out or wanted too much money, etc., or moved on by the time the pilot was to be shown for a potential series). Examples of re-filed/re-cast pilots include (this doesn't necessarily mean a full re-film): "Buffy the Vampire Slayer" and "Full House". Sometimes minimal scenes are changes and little things cut, like the original "ALF" pilot (which I think has some positives that shouldn't have been cut). Other times a pilot may have had good idea or premise but major changes were needed, meaning a whole new pilot. Sometimes two or three versions of a pilot will be done and none of them will air. An example of that was a 1960's thing called "Man on the Beach", which had two (maybe three) pilots filmed. One scored by Jerry Goldsmith and another by Billy May; never have aired. I don't think anybody outside of those who worked on it, have seen either. These days networks still don't pick up a number of pilots (probably half of which never air) but when they are interested in something, typically they'll order half a season or even a full season, so no "pilot" in the old sense, is needed. Though there have been series that filmed half or more of a season and didn't air at all (there was a UPN series, for example, that filmed I think thirteen episodes, and the plug was pulled and it never aired; don't recall the name off hand). There are even series where one episode might air and the rest, though filmed and ready, are not aired because it bombed I[]so badly[/I]. Two examples include: "Public Morals" A detective series that so offended public viewing morals, only the first episode aired out of thirteen made. "Heil Honey, I'm Home" What's funnier than making a series about Hitler and his wife? How about a comedy series? And what would be even worse? Making and airing it in a country Hitler almost wiped off the face of the Earth. You can imagine, it didn't last long. In fact, on episode out of eight, was shown. There have also being series ordered -- I don't know how often this happens -- that get canned in the middle of filming episodes, even though ordered as a series. One such example was a mid 1990's potential series trying to capitalize on other shows at the time like "Nash Bridges" and Martial Law"; it was called "Lawless" and the networked cancelled it while episodes were filming. One director told me none were completed, but by some miracle, one episode was and it aired. (coincidently, Joel Goldmsith was working on this failed series and also submitted a demo for a season six theme for NB).
The Big Bang Theory had two pilot episodes, the first one was never aired. It still featured Sheldon and Leonard, but the tone was much darker, the supporting cast was different and the apartment set was kind of grim (though probably more realistic) compared to what they used for the rest of the series. Search for Big Bang Theory Unaired Pilot on YouTube, it is quite bizarre.