The burner on a single-stage furnace has two settings. Either on or off.
When there is a call for heat from the thermostat, the furnace will come on at full power. It will run at full capacity until the heating call is satisfied and then shut itself off.
In order to maintain the temperature in the house, the furnace will repeat this cycle every time the thermostat sends a heating call to the furnace. The result is somewhat uneven heating throughout the house. The furnace will provide blasts of warm air that provide temporary comfort, but does not do a great job of maintaining a consistent temperature throughout the house. In that way, a single-stage furnace is not very efficient. But, it is the most affordable option.
The burner in a two-stage furnace can turn on at two different levels. Different burners are programmed differently. But for example, the burner may be programmed to run at 60% or 100% capacity.
Two-stage furnaces have longer, slower heating cycles that provide much more consistent and even heat throughout the home. This results in increased comfort and efficiency.
The longer cycle also provides better air filtration, as the air in the house will cycle through the furnace air filter more times in a day.
Two-stage furnaces are a balance between cost and value. They are more expensive to purchase than a single-stage, but will provide increased comfort and efficiency.
On a modulating furnace the burner has many possible levels it can turn on too. For example, it may start at 40% capacity and increase in increments of 0.5% up to 100% capacity.
Modulating furnaces provide maximum comfort and efficiency because they usually run continuously at a very low setting. The temperature of every room remains consistent because of the continuous operation and constant airflow.
Modulating furnaces are superior to two-stage and single-stage furnaces, but being the most efficient and highest performing, they are also the most expensive.
Multi-speed ECM blower motors have the ability to turn on at a handful of different CFM (airflow) outputs. This provides increased comfort and efficiency because depending on what is required, the furnace is able to adjust the CFM output.
Variable-speed blower motors are similar to multi-speed blower motors, but instead of just a handful of possible CFM outputs, the blower motor has many different possible outputs and can adjust and finetune itself to provide maximum comfort and efficiency.
If you plan to stay in your current home for more than 5 years, you may want to consider investing in a modulating variable-speed furnace. It will pay for itself through savings in around 3.5-5 years, and you will have 15+ more years of ongoing heating savings.
If you are unsure how long you will be living in the house, a two-stage furnace will provide a good balance of value to investment. Two-stage furnaces come with either a multi-speed blower or a variable-speed blower. If you choose a variable-speed blower motor it will pay for itself through electrical savings in around 2-3 years.
If you are flipping the house, plan to move, or will be using the furnace as a back up heat source, a single-stage is the most cost effective and will do the job.