A variable-speed furnace blower adjusts its speed dynamically based on the temperature, while a multi-speed blower has a finite number of motor blower speeds, usually two. Both options are more efficient than conventional single-stage furnaces.
Multi-speed furnaces typically have a high and low setting, though some models have significantly more settings. This allows the blower to stay on a lower setting for the majority of the time and kick into high during extreme cold. This setup is more energy efficient than having the blower on at a single speed whenever the thermostat dips below its minimum temperature setting.
Variable-speed furnaces, on the other hand, respond to incremental changes in the need for heat. Typically, this means that they run nearly constantly on a very low blower speed, which has many advantages. It is the most energy-efficient setup for a conventional furnace, and having the blower on low speed means that they are also typically much quieter than single-stage or multi-speed furnaces. Additionally, constant airflow allows homeowners to have much greater control over humidity levels in the home. This also means that air is continuously running through the filtration system, resulting in cleaner air. Incremental changes in blower speed also allow the furnace to give the home a more consistent temperature.
Variable-speed furnaces are the more expensive option in terms of upfront cost, but the increased energy efficiency may balance this additional initial cost.