It's the same time, but we need to write the time fully to see that.
Suppose Dorothy and her dog Toto are in Denver Colorado and it is 9AM.
We write it as 09:00 MST, where the 'MST' denotes Mountain Standard Time.
Or more fully as 09:00:00-07:00 in standardized
ISO 8601 notation, which means we have subtracted 7 hours from Universal Coordinated Time (UTC).
Now she and her dog are magically transported to Kansas City (instantaneously), where it is 10AM, or rather 10:00 CST, with 'CST' for Central Standard Time.
Again more fully 10:00:00-06:00.
Both are also written as 16:00:00Z, which is the time that a clock at the zero meridian (Greenwich, England) shows.
So even though the local clock shows a different time than Dorothy's watch, which really represents the altitude of the sun, it really is the same (UTC) time.
It's similar to how degrees Fahrenheit are converted to degrees Celsius. It's a different number but the same temperature.