There's no black and white definition of AC and DC servo but generally a DC brushless servo uses trapezoidal ("6 step") drive current waveforms and an AC (brushless) servo uses a sinusoidal current. If you drive the motor and look at the phase voltages, so you find an AC servo produces a fairly sinusoidal voltage and a DC servo produces more of a wobbly trapezoidal (rectangular) voltage. A DC brushed motor has just 2 terminals and is driven by a DC current.

Must admit, that machine of yours sounds more like a closed loop stepper. There are 2 quick tests you can do to check. A stepper will feel lumpy when you turn it by hand with the motor disconnected, whereas a true servo will run freely. You could also remove the belt to show that the noise is indeed due to the belt. Having said that, the belt shouldn't be making a racket....