I don't find the question entirely clear, but...
The makers of TOS were deliberately vague about how far in the future the series was set; the original proposal said it could be anywhere from 1999 to 2999. And references in the series conflicted. "The Squire of Gothos" implied that the series was somewhere around the early 28th century (since light from events in the early 1800s was only just reaching Trelane 900 light-years away); but "Space Seed" suggested that the series was more like 200 years after the late 1990s, and "Tomorrow is Yesterday" hinted that it was roughly 200 years ahead of the then-present. But "Metamorphosis" established that Zefram Cochrane had been lost 150 years earlier at the age of 85 -- which means, given that scientists' great breakthroughs usually come early in life, that warp drive had probably been around for at least 200 years at that point, suggesting a date further in the future.
Star Trek: The Motion Picture
bumped it forward a bit as well, having Decker say that the Voyager 6
probe was lost over 300 years earlier, which would've put the movie in the late 23rd century at the earliest. The Wrath of Khan
was the first Trek production to explicitly state (in the opening caption) that the series took place in the 23rd century.
But where in the 23rd century was still an open question. There were two schools of thought among fans and tie-in authors at the time. Some just assumed the series took place exactly 300 years ahead of when it aired, putting it in 2266-69. Others tried to reconcile the 23rd-century reference with the "200 years" references, and put it in the first decade of the 23rd century, typically 2206-09 -- which would be only about 210 years after the Eugenics Wars, fitting the "Space Seed" reference (though requiring Cochrane's warp breakthrough to happen relatively early, like in the first decade or two of the 2000s). This latter assumption was used by the 1979 book Star Trek Spaceflight Chronology
(interestingly, predating TWOK), and was followed by a number of Pocket Books' novels in subsequent years.
When TNG came along, it was initially relatively vague about the timing, stating only that it was in the 24th century, with behind-the-scenes materials claiming it was some 78 years after the TOS movie era (consistent with Admiral McCoy's age in the pilot). But in the first-season finale, "The Neutral Zone," we got our first explicit Gregorian calendar date for any Trek production: the current year was stated to be 2364. Which blew the Spaceflight Chronology
dating scheme out of the water, since it was consistent with the other theory that TOS had taken place in the 2260s and the movies in the 2270s-90s. But that was canonical now, so ever since 1988, that's been the official dating scheme for Star Trek