You keep saying things like "tiny bit different time." No, the clock on the eastern edge of the time zone is the same as the clock on the western edge. If it is 12:30 PM in the Eastern US time zone, it's not 12:05 in Indiana, 12:30 in Pennsylvania, and 12:55 in Maine. It's 12:30 across the whole time zone. That's sort of the whole point of having the time zones in the first place: to sync everyone up in that area, while still allowing everyone to hit "noon" roughly when the sun is overhead in their own area.

When you cross into Central, the clock will read 11:30. So in that sense, yes, the time is an hour different just because you cross that magic border line.

I think what you are really after though is whether or not the sun is in a different position, and the answer to that is yes. Lookup sunrise/sunset times in various cities in the same time zone, and you'll see they vary slightly. So again, in the eastern time zone, sunrise today in Indianapolis was 7:30 am, in Pittsburgh it was 7:05 am, and in Boston it was 6:28 am. All of them hit 7:30 AM at the same time, but the sun position in the sky can vary across the same time zone.