EF = Elecronic Focus, this is the name of Canon's autofocus mount. "II" means the second version of the lens.
EF-S = Canon's designation for EF "short back focus" lenses designed to satisfy the APS-C crop factor
EX = Sigma marketing term, denotes a higher build level. DC means the image circle is only covering APS-C ("crop").
HSM = Sigma's designation ultrasonic motor.
AF-S = Nikon's designation that the lens has the focusing mechanism in the lens, as opposed to being driven by the camera body. The mechanism is usually ultrasonic.
ED = Nikon's designation for glass with
high extra-low dispersion.
VR = Nikon's designation for image stabilization in the lens ("Vibration reduction").
OS = Sigma's designation for image stabilization.
L = Denotes Canon's high-end lenses ("luxury")
IS = Canon's designation for image stabilisation
USM = Canon's designation for ultra-sonic motor motor