I believe standby and sleep and suspend are three names for the same thing. Currently questions are split between the tags.
This is status-declined. As slhck pointed out, each one of these tags has a different meaning and connotation, and are used differently. Standby is different than sleep, for example.
standbyis the general term for a standby mode that not only computers have (monitors, external hardware, etc.), but they don't have a "sleep" or "suspend" option.