Monoclonal antibodies (mAbs) are a focus in vaccine and therapeutic design to counteract severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and its variants. Here, we combined B cell sorting with single-cell VDJ and RNA sequencing (RNA-seq) and mAb structures to characterize B cell responses against SARS-CoV-2. We show that the SARS-CoV-2-specific B cell repertoire consists of transcriptionally distinct B cell populations with cells producing potently neutralizing antibodies (nAbs) localized in two clusters that resemble memory and activated B cells. Cryo-electron microscopy structures of selected nAbs from these two clusters complexed with SARS-CoV-2 spike trimers show recognition of various receptor-binding domain (RBD) epitopes. One of these mAbs, BG10-19, locks the spike trimer in a closed conformation to potently neutralize SARS-CoV-2, the recently arising mutants B.1.1.7 and B.1.351, and SARS-CoV and cross-reacts with heterologous RBDs. Together, our results characterize transcriptional differences among SARS-CoV-2-specific B cells and uncover cross-neutralizing Ab targets that will inform immunogen and therapeutic design against coronaviruses.