Yes, most people say "dead body". "Corpse" is mostly used in books and movies. It is to be noted that "corpse" is only used for human beings. Examples with corpse - 1. The startling discovery of a corpse required a call to the police. 2. A battlefield strewn with corpses.

'corpse' is more a legal/scientific/medical term for a body. In general conversation you'd almost always use the term 'body'. It sounds much more polite and caring. 'corpse' sounds rather cold or remote as the term does not carry any sense of emotional attachment of the speaker to the 'body'. 'body' doesn't always carry this sense of emotional attachment or caring, but it can. Corpse is far more distant and colder a term. As an example, if a friend died, you would never use the term 'corpse' yourself. However the medical examiner may use either term - 'body' or 'corpse'.

A corpse is ONLY used to reference a dead person. Body is used for the living or dead but usually we will say dead body if the individual is no longer alive.