A virus in the first place is not even considered living...nor is it non-living. It has properties that could make it partly alive (coat proteins, RNA, etc)..but it does not have a nucleus. By definition all living organisms have a nucleus at cellular level. So by rights a virus is not classified as being alive, nor is it dead.
Anyway...Human Immunodeficiency Virus is a virus that attacks the T-helper cells of the immune system..as a result lowering the body's resistance to pathogenic agents. Acquired Immunodeficiency Syndrome is actually a generalization of the diseases caused by opportunistic infections due to lower resistance. So in theory, if you have HIV...but you can fight of opportunistic infections, then you could be said to be free of AIDS.
Complicated is'nt it?