SARS - disease or syndrome?

When I was in high school, my biology teacher told us that the difference between a disease and a syndrome was that a disease could be fatal, whereas a syndrome could not. When we asked about AIDS, he said that AIDS itself did not kill, but lowered the body’s resistance to fatal diseases.

SARS, according to its name, is a syndrome. But it would certainly seem to be fatal. Is it an appropriate name?

Taken from dictionary.com.

syn·drome n.

A group of symptoms that collectively indicate or characterize a disease, psychological disorder, or other abnormal condition.

By the way, AIDs can kill you on its own.