Labs are now trained to avoid the positive-negative nomenclature, as it implies diagnosis which most lab tests are incapable to do on their own. Only licensed medical professionals can diagnose. Nowadays it's reactive or non-reactive, and other words depending on the kind of test. Specially with modern treatments, lot's of people live with HIV but would be nonreactive in all tests if they're under treatment. They still would be infected with the virus but won't be detected by labs, and probably would never get ill.