Surface stains are stains sit on the enamel layer of our teeth. The most common sources of surface stains include chromogenic bacteria (stain-causing bacteria), tannins from coffee and tea, and accumulated food particles that stick to our tooth's surface. The best way to prevent and remove surface stains is to brush and floss regularly. In essence, the colored biofilm needs to be scrubbed away.
Intrinsic stains are stains within the inner structure of your tooth. A tooth can develop intrinsic color changes as a result of trauma or injury, or exposure to certain antibiotics during infancy or childhood. Teeth (namely dentin) tend to become intrinsically darker over time.
There are a plethora of over-the-counter tooth whitening agents. These agents typically work via two basic mechanisms of action – polishing (let's scrub that tooth clean) or bleaching.
Polishing is usually accomplished via whitening toothpastes, which contain a polishing agent (an abrasive compound, for instance, such as silica). These molecules help scrub away stubborn surface stains when brushing.
Abrasives should be textured enough to remove plaque and stains, but not abrasive enough to damage your enamel. Common abrasives (more commonly know as):
Bleach is usually applied through the form of whitening pens, whitening gels and trays, or whitening strips. The oxidizing agent (the molecule responsible for breaking up color bonds) is Hydrogen Peroxide or Carbamide Peroxide (which in turn, releases ~33% hydrogen peroxide).
At its core, the basic mechanism behind teeth whitening is the same as that behind a Tide pen or bleaching your hair.