Canon = Ultra Sonic Motor (USM)
Nikon = Silent Wave Motor (SWM) (Lenses with SWM are designated AF-S)
Sigma = Hyper Sonic Motor (HSM)
Tamron has no similar technology, but for the purpose of answering if Tamron lenses are able to auto-focus on D40/40x/60, Tamron has released a series of lenses with a built-in motor. The models with a built-in model are:
Tamron 17-50mm f/2.8
Tamron 18-250mm F/3.5-6.3 and the
Tamron 70-300mm F/4-5.6.
Take note that you must buy the models that indicate that they have a built-in motor in them, as the older models do not have such a motor. The model name will also give you a clue:
Tamron 70-300mm F/4-5.6 WITHOUT built-in motor: Model A17
Tamron 70-300mm F/4-5.6 WITH built-in motor: Model A17N II
I don't know much about Tokina though.