In modern times we have time zones and such to distinguish all that, but were people in the times before rapid travel aware of these differences as well? They knew that the Earth was round, so it would seem obvious enough that the sun rotating around the earth would shine on different parts at different times, but as far as I know they couldn't travel fast enough to confirm this personally and there are plenty of things that seem "obvious" to us now that actually took a lot of effort and research to find out.
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.
There's an FAQ section on "Language, Symbols, and Time". "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? 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 /u/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).
When did people understood the concept of time zones (that when it's morning in america it's night in Europe)? by jschooltiger. This is their fuller answer on Hipparchos.
I will also note