Here's the important part.....
non proportional thermostats use an "on/off" approach and usually have a 1 or 2 degree (or more in cheaper ones) "slop". They turn on 100% when the temperature falls a degree or two below the set point and they stay on until the temperature gets to the set point, and often have momentum and go 1 or more degrees beyond the set point. This means that if you set your thermostat at 80 degrees your actual temps can vary between as low as 76-78 degrees and as high as 82-84 degrees. A roller coaster ride for your animals
proportional thermostat more like a light dimmer with a brain constantly adjusting itself to maintain a much more precise temperature. The "slop" in proportional thermostats is usually measured in 1/10 degrees