In-Office Bleaching:  Bleaching may be done in the dental office using stronger concentrations of bleaching material than one would want to use on a long term basis at home.  Your lips and gums will be protected during the time the bleach is in contact with the teeth.  This in-office procedure can give a little "head start," with the patient  continuing with an at-home treatment, or it may be presented as a "quick and easy" one-time procedure.
      The dentist may or may not use a light. While the light systems are widely promoted by the manufacturers and user dentists, these treatments are generally more expensive and  there does not seem to be much, if any, evidence that they add to the effectiveness of the bleach. Dentists using the light will disagree, but independent studies have seen little difference.

Home-Bleaching Systems: These methods are designed to bleach  at home.  They are not inferior to the in-office treatments at all in my opinion.  In fact you may prefer to have the option of reapplying the bleach now and then after the initial course of whitening is finished.  An at-home bleaching system needs a way to keep the bleach on the teeth and there are several ways to do this.  These  methods include:

Tray systems in which a tray is filled with bleach and worn to bed or during the day:  The effectiveness will depend on the fit of the tray (It should be closely adapted to the teeth) and the concentration of the bleach;

Over-the-counter bleaches that are worn via thin bleach-coated strips: Yes, these work very well, are easy to use and are relatively inexpensive.  Those found on store shelves work but you should there is a professional strength made that  be ordered only through dentists.  I was very happy with the strips I got at the drugstore, frankly.

Home Paint-on Bleaches:  This method is hard for some people to use.  But there is one I really like and use myself: It is  Crest "Night Effects,"   This thick bleaching material  dries on the teeth so it is able to stay in contact with them for a while.  The trick  here, is to dry your teeth (e.g., with a cotton swab) before painting the material on with one of the little brushes that is supplied.  Otherwise the bleach will not stick to the tooth and the procedure will be messy and frustrating.  Removal is best done by scraping the film from the tooth (with a tooth pick) and then brushing.  If you don't like the fuss you will prefer the strips.

Some paint on night time gels are not good at all since they don't dry or solidify on the teeth.  These look like little nail polish shaped bottles with a brush  in the cap.  There is nothing to keep them in contact with enamel and so saliva just dilutes and washes them away.   I do not recommend or use these.