"[TOS] was a show designed for syndication. This meant that episodes needed to be entirely self-enclosed, with characters returning to the status quo at the end of each adventure so that networks could play them in any order, using a handful of Kirk’s escapades to neatly plug holes in their schedule whenever they needed to.
With The Original Series, it’s possible to dive into any episode (bar, possibly, the series’ lone two-parter) and quickly grasp not just the plot, but the dynamics between the three lead characters. McCoy is never shown to grow more tolerant of Spock’s stoicism, for instance – we assume that their friendship is growing stronger over time, because that’s what friendships often do, but there’s no real evidence of that within the show itself. No-one’s promoted or reassigned, the main characters are effectively immortal and past adventures are spoken of only in oblique terms even when villains like Harry Mudd do make a return appearance, many of which happened in the animated follow-up rather than the live-action show.
While we’ll never know for sure if the aborted sequel Star Trek: Phase II would have continued to tell isolated, stand-alone adventures, the Star Trek movies began to head down a very different path. Even when the films didn’t immediately follow on from one another, they began to embrace the show’s own continuity and build upon past events, allowing the characters to grow and change over time.
Likewise, 1987’s Star Trek: The Next Generation, which debuted while the original crew were still riding high at the box office, almost immediately went out of its way to push beyond the confines of syndicated TV. During its pilot episode, Encounter At Farpoint, we see the main cast encountering one another for the first time - along with a few reunions - and as they get acquainted, we come to know them too. Early on the story chooses to follow Riker, using him as our proxy while he tours this unfamiliar Enterprise and meets its austere new captain. It’s a measured and deliberate premiere that takes time to make its audience familiar not just with the full ensemble cast, but also with the ship they’ll be calling home. (By contrast, we still don’t know for sure how prime-universe Kirk, Spock and McCoy first met.)
As the story goes, TNG’s original remit would have been to make a clean break within the series canon, never acknowledging The Original Series. James T. Kirk, it was felt, would have long ago been consigned to history as just another heroic Starfleet captain. In practice, this conceit is discarded barely half an hour into the pilot, when DeForest Kelley’s unnamed character appears to give the ship and its crew his blessing. Given that the very next episode would go on to be a sequel of sorts to classic story The Naked Time, the message was loud and clear: The Next Generation would be unrepentantly building upon what had come before."