See Figure 1 on page 2 of lecture notes 2. Each B cell as a single specificity.
Further diversity is achieved by isotype switching and somatic hypermutation.
Thus although each B cell response is specific, the response to the pathogen involves numerous B cells, different antibody isotypes with different binding affinities. Alternative RNA splicing. See Figure 12 on page 12 of lecture notes 4. See functions of different antibody isotypes on pages 5-7 of Antibody Structure and Function lecture notes ii.