This might be Home Planet, developed by John Walker. The second release was published as freeware in 1994, and ran on Windows 3.1. (I haven't been able to track down information about the previous version.)
Its main screen (which is also usable as a screensaver) shows the day and night areas of the earth's surface, albeit without time zones:
The one I know is GeoClock, though it looks like its website is no longer in operation.
It can still be found in Simtel archives, along with extra maps. You can also see an older version in action on the Internet Archive.
It probably wasn't this: Amateur Radio Clock. But this type of clock application is popular with ham radio operators.
What you're describing sounds a lot like a software version of a Geochron. These are mechanical maps of the world with light and dark bands that move across the projected planet.