Is this the only basic difference in the "prime universe" timeline? Just 60 years between some of the suggestions mentioned by characters in TOS, and the "official" timeline?
No, the 60-year discrepancy is between the two fan
theories that existed prior to TNG -- the Spaceflight Chronology
timeline that put TOS in 2207-10, and the alternative fan theory, later made official, that put TOS in 2266-69. Those were both outside interpretations based on
evidence from TOS, but neither of them came from
TOS itself. TOS was intentionally vague about the setting. Even the two big "200 years" references are vague as to the actual decade -- is it 200-ish years after the Eugenics Wars of the 1990s or 200-ish years after "Tomorrow is Yesterday" in the late 1960s? And of course those clash with the "Squire of Gothos" reference and the TMP reference, and the "Metamorphosis" reference doesn't make things any clearer.