What is benefit of brush less dc motor and brush less ac motor. And when we use bldc and when blac? What is different of them? What about the power saving too.

Electronically commutated motor - Wikipedia, the free encyclopedia

The link to BLDC is in the citation as well.

I'll add, that a brushless AC motor is basically a 3 phase motor. It gives enormous energy savings over a PSC motor in a single phase application.

Brushless DC has many forms.

Why would you want to use a brushless DC motor for say a home HVAC system?

And

A brushless AC motor wouldn't work for a floppy positioner, nor a turbomolecular pump that operates at about 40,000 RPM.