Here is an example test which checks specifically for virus induced antibodies: <https://monitormyhealth.org.uk/covid19-antibody-test/>. Non-profit Testing for All also used to sell similar tests, but they have stopped operating.

In contrast this test does not distinguish between virus and vaccine as the cause: <https://onlinedoctor.superdrug.com/coronavirus-antibody-test...>.

I don't have a better approach than checking the descriptions of individual antibody tests. But I know the distinction is real, because IIRC the ONS (statistics body) used tests which distinguished, when they ran their ongoing study.

Back then the Red Cross would do free antibody tests for anyone who donated blood. There were two. One could not distinguish between antibodies from an infection vs. vaccine, and came back in a day or two. The other did, and took longer.