Brush type generator
I don't know modern Airbuses, but I suspect you are thinking of the starter motor, and DC motors have to have brushes to work.
AC generators (Alternators) have been brushless for ages.
AC generators (Alternators) have been brushless for ages.
They are AC motors with integrated electronics to convert the DC supply to AC for the motor. The electronics are now sufficiently efficient, light, compact and reliable for the description "Brushless DC" to be not that unreasonable. The AC's frequency can also be varied to get any desired motor speed.
The brushless alternator is very clever yet simple old technology. It is two alternators on one shaft. One generates the field for the main one and is inside out so it's field can be varied without brushes. This allows control of the field of the main alternator and thereby it's output.
I am not an expert but I believe that the above is substantially correct.
PDR