How was tooth whitening invented?

An orthodontist wished to use hydrogen peroxide to control plaque accumulation on his patients' teeth.  One "side effect" of leaving hydrogen peroxide on teeth was that they became whiter.  This is how a multi-billion dollar industry was born.

Why is tooth whitening also called bleaching?

Bleaching is just another term for using an oxidizing agent.  In your laundry machine, the oxidizing agent is most often sodium hypochlorite, a.k.a. Chlorox or household bleach.

The two most popular oxidizing agents in dental tooth whitening are hydrogen peroxide and carbamide peroxide.  Carbamide peroxide takes roughly three times as much concentration to equal the effect of hydrogren peroxide, but is more commonly used because of the promise of less sensitivity.