A rheostat is basically reducing the heat that is given off by the heating device. So say your heat mat is a 20W a rheostat can be used to reduce the heat by say 10W so your device is giving off 10w. This will not change no matter how hot your house gets so say 10w raises the room temp by 10C. If your room temp is at 0c you will get 10C however if your room is at 30C you will get 40C. This in my opinion is not a reliable way of controling the temperature.
A thermostat on the other hand controls heat differently. Your cheaper ones switch themselves on and off as the temperature increases or falls. This is done basically by a device in the thermostat continually measuring the temperature( an error detector) if it detects a difference in the set temperature and the actual temperature it switches the heat mat on or off to correct the error. They will usually keep your temp within two degrees of set temperature.
Then there is the expensive type which are not necessary but they work great. These are pulse proportional thermostats. Now the best way to explain these is using Pulse With Modulation to control a motor, by switching the motor on and off very quickly you are able to reduce the speed without reducing the torque( turning power). Now this thermostat works in the same way instead of the cheaper version it actually turns the heat mat on and off very quickly in pulses. So your temperature is reduced if your off time is a bigger pulse than your on time and vice versa. These pulses are only milliseconds long so provide almost an almost accurate temperature to the one you set with no variations.
And finally you get a combination of a rheostat and a themostat. These are called dimming thermostats. They work in much the same way as a pulse proportional thermostat but instead of acctually switching the device off they dim it down meaning that you can use them with lights so that your light does not keep turing itself on and off.