The nasal swab test detects an active Covid infection.
The blood draw tests that I know about detect antibodies against Covid-19 which indicates your body has had more than 7 days to make these, so you have had active Covid-19 virus quite a while, or more likely, have gotten over Covid quite some time ago.
This article comments on how accurate that blood test is, and how some people overcome Covid with T-cells, and may not have detectable antibodies.
There are saliva spit tests for active Covid-19. I only know they are 5-10% less accurate, and so far take a long time because they have to be sent off site to get the final result
