Swab Test (PCR)
Works by detecting the presence of the virus' genetic material (RNA). The biggest difference being that it can detect early and onset infection with most accuracy with results available in a few days.
Blood Test (Antibody/Antigen)
Works by indirectly detecting the virus by measuring your body immune response (igM, IgG) to the virus. This test is typically used to detect if you have had the virus in the past and now show immunity to certain strains of the virus.