What are different cataract operations & procedures?

Variations. The modern technique of cataract removal is basically that of ultrasonic removal of the cataract and microscopic substitution of a proper calculated lens. There are minor variations in the technique and some differences in lens design. But the basic principals are the same. Older techniques of removal and non-mechanical removal are largely obselete except in third world countries.
Anesthesia differs. The majority of cataracts are removed by phacoemulsification, a type of ultrasound technology. However, about 50% of the doctors in the us use a needle to numb the eye and 50% use eye drops. With the needle, the sensation, the vision, and the movement of the eye is numbed. With drops, only the sensation. There are pros and cons of each, which you should discuss with your eye md.