These words can cause confusion when used to talk about the time of an event. When some people say “Let’s move the meeting back”, they mean earlier.
Other people understand it mean later. The opposite goes for ‘forward’ and ‘up’. To most people, “Let’s move the starting time forward” or “My interview time has been moved up” would mean later, but could still be confused as meaning earlier.
The safest bet is to spell out the meaning clearly: “My interview time has been moved ahead one hour, from 1 to 2”, or “Let’s move the meeting a day earlier.”