You're right...most refrigerators have one compressor.
The way most of them work...the Thermostat is set to control the temperature inside the fridge. This drives the compressor to work...which actually cools the evaporator in the freezer. A fan blows some of the cold freezer air through a trap door into the refrigerator. The trap door is usually labeled FREEZER Temperature Coldest to Warmest... It clamps down to lower the FREEZER temp....and opens to raise the FREEZER temp. There is also a timer circuit in a "frost-free" refrigerator...which cycles a couple of heat strips...one near the freezer door, and one under the evaporator coils...this is an automatic defrost cycle which lasts a couple of minutes and then the system resumes to go back to chilling.
If your compressor is running all the time...either the compressor isn't charged properly, or your defrost isn't working right...causing the airflow to the refrigerator section to be blocked. ( I say this only because your Freezer is cold) IF it shuts on and off normally, but the fridge temp is higher than set for...you could have a thermostat problem...but your timer could be screwing up too...and going into an extended defrost cycle...so you have to trouble shoot.
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Go there and click on Repair Help. If I remember correctly, it walks you through some tests to find out what part needs to be replaced...and they sell parts too..