"Pilot" seems to have been genericized to the point of basically just being used as an umbrella term refering to the first episode of any series, but as fuzzygobo mentioned, back in the older days of television, a pilot was usually totally separate from the rest of the series' proper, and more often than not used as a presentation to the networks to show them what exactly this show was they should consider buying and adding to their lineup.
One infamous example I can think of off the top of my head is THE MUNSTERS, it's pilot differed significantly from the actual series for two major reasons: 1) It was actually filmed in color, as opposed to black-and-white like the series was, and 2) Different actors played Lily (whose name was actually Phoebe) and Eddie, neither of whom really had any connection or chemistry with Fred Gwynne or Al Lewis (and the kid played Eddie more like an actual feral wolfchild, rather than an all-American type boy who just happens to be part werewolf like Butch Patrick). The pilot obviously never actually aired on broadcast television, but again, it gave the network an idea of what this show would be like, and what changes could be made before going to series . . . I personally wouldn't have minded if the series remained filmed in color, but recasting Lily and Eddie with Yvonne De Carlo and Butch Patrick, respectively, made a world of difference.
In some cases, a series' pilot is actually an episode of previous show that's used as a setup for something of a spinoff, such as an episode of THE DANNY THOMAS SHOW in which Danny gets arrested by a country bumpkin sheriff who's also the town judge, Justice of the Peace, and mayor lead to the creation of THE ANDY GRIFFITH SHOW. In turn, the Season 4 finale of THE ANDY GRIFFITH SHOW dealing with Andy seeing Gomer off to join the Marines served as the backdoor pilot for the spinoff GOMER PYLE, U.S.M.C.
Of course, that's not to say all series have taken either of these approaches . . . in some cases, even back then, the pilot that was filmed did, indeed, end up being used as the proper opening episode of its series' proper - and you can usually tell, because these are almost always what are known as premise pilots: where basic concept of the show is all spelled out and established in said opening episode, such as BEWITCHED showing us Darrin learning that Samantha is a witch on their wedding night, or I DREAM OF JEANNIE showing us Tony ending up on an uncharted desert island, finding a fancy bottle, and ending up freeing Jeannie, or GREEN ACRES showing us Oliver buying a farm to live out his dream of being a farmer and getting away from the rat race of the city.
And then, every once in a while, you have an unusual case like SEINFELD. What ended up becoming that series' pilot as well as proper opening episode was intended to be a one-off special by Jerry Seinfeld and Larry David that basically fictionalized the process of how a comedian gets his material, but this special ended up being turned into one of the biggest smash hits in TV history.
Obviously, it varies depending on many different factors, but again, in most cases, "pilot" is another one of those examples of a word becoming genericized like "Kleenex" and the like.