When someone is deceased, they are dead — not dying or even just about to die. They are dead.
The word deceased has been around since the 15th century, however, when people talk of someone's having died, they rarely use deceased in conversation. For example, if you ask someone how their dog is and their dog is recently deceased, they'll most likely use a less technical phrase such as "no longer with us," or "passed away." The word deceased is more formal, and most often used in the documentation of death or in legal situations, as in "we are here to read the will of the deceased."