Antibodies and helper T cells play important roles in SARS-CoV-2 infection and vaccination. We sequenced B– and T-cell receptor repertoires (BCR/TCR) from the blood of 251 infectees, vaccinees, and controls to investigate whether features of these repertoires could predict subjects’ SARS-CoV-2 neutralizing antibody titer (NAbs), as measured by enzyme-linked immunosorbent assay (ELISA). We sequenced recombined immunoglobulin heavy-chain (IGH), TCRβ (TRB), and TCRδ (TRD) genes in parallel from all subjects, including select B– and T-cell subsets in most cases, with a focus on their hypervariable CDR3 regions, and correlated this AIRRseq data with demographics and clinical findings from subjects’ electronic health records. We found that age affected NAb levels in vaccinees but not infectees. Intriguingly, we found that vaccination, but not infection, has a substantial effect on non-productively recombined IGHs, suggesting a vaccine effect that precedes clonal selection. We found that repertoires’ binding capacity to known SARS-CoV-2-specific CD4+ TRBs performs as well as the best hand-tuned fuzzy matching at predicting a protective level of NAbs, while also being more robust to repertoire sample size and not requiring hand-tuning. The overall conclusion from this large, unbiased, clinically well annotated dataset is that B– and T-cell adaptive responses to SARS-CoV-2 infection and vaccination are surprising, subtle, and diffuse. We discuss methodological and statistical challenges faced in attempting to define and quantify such strong-but-diffuse repertoire signatures and present tools and strategies for addressing these challenges.