Pointing out the FAQ and previous answers is not to discourage further questions, especially because some of the previous answers were about time zones specifically, not time differences. Since the posts are generally archived, such questions can go here.
In addition to jschooltiger's reply, which was a fuller answer on Hipparchos:
There's an FAQ section on "Language, Symbols, and Time" at https://www.reddit.com/r/AskHistorians/wiki/faq#wiki_language.2C_symbols.2C_and_time . "Clocks" at https://www.reddit.com/r/AskHistorians/wiki/language#wiki_clocks points to
- "At what point did humans understand the existence of timezones - i.e. that the sun didn't rise and fall the same way everywhere?" at https://www.reddit.com/r/AskHistorians/comments/7ahhv3/at_what_point_did_humans_understand_the_existence/ by /u/restricteddata. He quoted Magellan's people being baffled that they'd lost a day going west around the world, which was only explained to them later. There's more by jschooltiger, noting that Hipparchus of Nicaea not only knew of different solar heights based on longitude, but proposed a procedure to determine it (thwarted by not having technology to do it).
I will also note
- "How long did it take Columbus to realize he wasn't in Asia?" at https://www.reddit.com/r/AskHistorians/comments/sfzx1/how_long_did_it_take_columbus_to_realize_he_wasnt/ . /u/jabbercocky writes, "In Columbus's Book of Prophecies - yes, really - he says he was five and a half hours away. However, within less than a year, he testifies to the King and Queen that he was nine hours away!" Not only measuring longitude, but measuring it in hours. (He used the start and end times of eclipses.)
- "Did the early Europeans (flat-world era) have any inkling of times zones. If so how did they explain these things..." at https://www.reddit.com/r/AskHistorians/comments/wpro0/did_the_early_europeans_flatworld_era_have_any/ : Crevecoeur notes that in Dante's Purgatory, Dante notes that the sun was at different heights on Mount Purgatory, Jerusalem, and the Ganges. The passage is at http://www.poetryintranslation.com/PITBR/Italian/DantPurg1to7.php#PurgCantoII1 . I find it hard to interpret, and I wonder whether the explanation at https://digitaldante.columbia.edu/dante/divine-comedy/purgatorio/purgatorio-2/ has a correct diagram.
- "Did people in ancient and medieval times know about time zones?" at https://www.reddit.com/r/AskHistorians/comments/4z5u3y/did_people_in_ancient_and_medieval_times_know/ : qed1 cites Martianus Capella, Marriage of Philology and Mercury (circa the 5th C AD). There was also Bede citing Augustine. Also, there was Roger of Hereford, writing in the 1170s, calculating longitudes of several cities based on an eclipse. (Inaccurately: he has Marseilles and Hereford 21 degrees apart when they're actually 8 degrees apart. Clock technology, amiright?)