The presence of frost on the inside of a freezer when it's turned off, but not on the outside, can be attributed to the difference in temperature and humidity between the two environments.
When a freezer is turned off, the temperature inside starts to rise gradually. As the warm air enters the freezer, any moisture or humidity inside the freezer begins to condense on the cold surfaces, especially on the walls and shelves. This is because warm air can hold more moisture than cold air, and when it cools down, it reaches its dew point—the temperature at which air can no longer hold all its moisture, leading to condensation.
The inside surfaces of the freezer, being colder due to its insulation and previous operation, cool the warm, humid air coming in and cause the moisture to condense on them. This is why you see frost forming on the inside of the freezer.
On the other hand, the outside of the freezer does not usually accumulate frost when turned off because it is exposed to the surrounding room temperature, which is likely much warmer than the inside of the freezer. As a result, the outside surface of the freezer does not cool down significantly to reach the dew point and cause condensation.
In summary, the difference in temperature and humidity between the inside and outside of the freezer when turned off leads to the formation of frost on the inside but not on the outside.