They're all slightly different, but yes they're looking for antibodies against specific parts of SARS-CoV-2, like the N protein [0][1]. I think the N protein ones are most common. I just did a BLASTp against SARS-CoV's N protein and there's maybe ~90% homology? So I would hope they're using a site that's different between the two. Or, there's an assumption that most people have not been previously exposed to SARS-CoV or others with similar N proteins.
> Also aren't antibodies effectively developed in a sort of random process?
Yeah, but there's only so many prominent features to a virus that you can make antibodies against.
[0] https://www.abcam.com/novel-coronavirus-igg-antibody-detecti... [1] https://www.ncbi.nlm.nih.gov/protein/QHW06046.1?report=fasta
Perhaps humans tend to have enough random antibody generation that they are likely to start mass producing most of the protein shapes that are able to bind to the virus? And as another commenter pointed out, there are not that many options to bind to.
I wish we had leaders that had the chutzpah to say things like, "look the science is inconclusive, so we won't arrest you, but please do the right thing and wear masks". But we don't. And also we have people spouting completely non-evidence based assertions like "if you don't force people to wear masks, then they won't". Which of course fuels assholes to flaunt not wearing masks, because now it's not about doing the right thing, it's about freedom.
https://www1.nyc.gov/assets/doh/downloads/pdf/imm/covid-19-d...
If instead we had done random sampling we could have been very accurately projecting the number of active cases pretty easily, but apparently we’ve mostly decided not to do that until now with the antibody studies.