SARS-CoV-2 provokes a robust T cell response. Peptide-based studies exclude antigen processing and presentation biology, which may influence T cell detection studies. To focus on responses to whole virus and complex antigens, we used intact SARS-CoV-2 and full-length proteins with DCs to activate CD8 and CD4 T cells from convalescent people. T cell receptor (TCR) sequencing showed partial repertoire preservation after expansion. Resultant CD8 T cells recognize SARS-CoV-2-infected respiratory tract cells, and CD4 T cells detect inactivated whole viral antigen. Specificity scans with proteome-covering protein/peptide arrays show that CD8 T cells are oligospecific per subject and that CD4 T cell breadth is higher. Some CD4 T cell lines enriched using SARS-CoV-2 cross-recognize whole seasonal coronavirus (sCoV) antigens, with protein, peptide, and HLA restriction validation. Conversely, recognition of some epitopes is eliminated for SARS-CoV-2 variants, including spike (S) epitopes in the Alpha, Beta, Gamma, and Delta variant lineages.