Hi,
Grinding involves the use of an accurately dressed, unitised wheel (or 'diamond lap' wheel) and comes under the most common guises of surface grinding (component oscillates from side to side under a rotating wheel to produce a flat surface) and cylindrical/universal grinding (both wheel and component rotate to grind a cylindrical surface). Various grit size/material is used to suit different requirements. Wheels can be dressed to suit a particular form if required.
The Lapping technique I am aware of uses a machine with a rotating bed. Components are placed on the bed within guide rings or rollers and allowed to rotate freely as the bed rotates. Lapping compound (oil and VERY fine grit) is applied to the surface of the rotating bed. The components own weight is enough pressure for this compound to polish the mating surface flat. As no excessive clamping force is involved an extremely flat surface can be achieved. An experienced operator is required to keep the machine bed flat...
The Honing technique I am aware of involves a set of rotating stones which can be adjusted within a certain range to grind out an existing bore/hole. The component is fed back and forth manually and the spindle speed is controlled by a foot pedal.
Not sure how Burnishing works, it has a similar use to honing, but I believe it uses a rolling/pressure action rather than an abrasive action. Produces a superb finish, but may be limited in terms of metal removal.
Polishing is done manually, usually to hide a mistake or draw attention away from the mistake by giving the component a uniform finish
DP