My 2 cents worth,
AC fans come in three major varieties, universal motors, capacitor run, and shaded pole motors.
Universal motors contain brushes and are generally high power. Common uses are items such as vacuum cleaners, blenders, electric drills, etc. They are often rated for intermittent use for short runs and for the size are high power. They are called universal as they work fine on AC or DC power. The exception is variable speed controllers do not run on DC. The motor is universal, the speed control is not.
Capacitor run motors are lower power than a universal motor, but higher power than shaded pole motors. They require a capacitor on one leg to start and run the motor. Common places to find one are the vent fan over a stove, portable box fan, or bathroom fan.
Shaded pole motors are a type of induction motor and are low torque. They are often rated for 100% duty cycle such as computer fans, microwave oven fans, bathroom fans, etc. They have no brushes. Due to the high inductive load, they often do not work well on an inverter.
Note that some bathroom fans are capacitor and some are shaded pole. This use is about the size that the transition from small shaded pole and larger induction motors takes place. A small AC fan that would fit in a spudgun chamber will most likely be a shaded pole motor.
Another small category is really a DC motor used with a rectifier. They have brushes and magnets. The most common place to find these are hair blow driers. They are again relatively high power and are not 100% duty cycle.
A note on motorcycle batteries and inverters. The cost of either item + a charging system is much more expensive than a 12 volt computer fan. Why bother.