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I prefer to think of a BLDC motor as any other DC motor. The difference between a brushed and a brushless motor is simply that in a brushed motor the commutation is done mechanically by the combination of brushes and commutator, and in a brushless motor it is done by solid state electronics. Physically they work the opposite way, the coils are fixed and the magnets spin, but they are still governed by the same equations that link voltage, current, RPM, torque and efficiency using the same set of coefficients, only the typical values of those coefficients are different to reflect the different construction involved.

The advantage of a brushless motor is that it eliminates the moving parts involved in the commutator. The point of contact of the brushes can skip (leading to arcing), requiring a spring pressure and consequent resistance to turning (which can be reduced by material choice but not eliminated) and introduces electrical resistance that lowers the motor's efficiency under load compared to a well designed solid state commutator that has resistances in the low milliohms or even lower. Obviously wear of the brushes and commutator is not a factor. Also in the case of an "in-runner" brushless motor, the windings are glued to the outer case of the motor making it easy to conduct heat away from the windings.

There are 2 flavors of brushless motor. Some use a sensor (hall effect or optical) to detect the orientation of the magnets, they behave almost identically to brushed DC motors (except with typically higher efficiency), while sensorless brushless motors try to determine the position of the magnets based on the behavior of the windings and the voltage induced by the spinning magnets. This doesn't work well at low RPMs so sensorless brushless controllers use a startup mode that works without feedback initially (very much like a synchronous AC motor) until there is enough information coming back from the windings to allow proper commutation. Because of this. motors with sensors have better low RPM behavior and can start reliably at high torque. They cost a little more because of the additional cost of the sensor. (But sensorless motors have improved over the past 2 to 3 decades. so I might be overselling the difference.)

- Rob.