In combined units, the freezer supplies cold air to both the freezer and the refrigerator. Cold air moves from the freezer to the refrigerator via a damper. The refrigerator setting controls how cold the air becomes in both the freezer and refrigerator.
There are many kinds of combined refrigerator and freezers. These include a side-by-side refrigerator and freezer, a top freezer refrigerator, a bottom freezer refrigerator, and a French door refrigerator, which has a bottom freezer but two refrigerator doors.
When the freezer is turned off, the compressor is shut off and cold air stops circulating from the freezer to the refrigerator. The refrigerator determines how long the compressor will run, but the freezer determines whether it is on or off. Therefore, the refrigerator won't work if the freezer is turned off.
In select refrigerator models, including older ones, the refrigerator controls may be entirely separate. Look for the dial, switch or button that can be adjusted to an "Off" position. This will shut off the entire unit, regardless of the switch's location, unless you can still hear the compressor working.