Step 1: Antigen-binding site. Both BCR and antibody are derived from the same rearranged variable (V), diversity (D), and joining (J) gene segments, therefore they share the same antigen-binding site. Hence (A) is correct.
Step 2: Epitope recognition. Since their antigen-binding sites are identical, they recognize the same epitope, not different ones. Thus (B) is incorrect.
Step 3: Genetic encoding. Both BCR and antibody are encoded by the same immunoglobulin gene locus. Hence (C) is correct.
Step 4: Mechanism of production. The difference between membrane-bound (BCR) and secreted antibody forms is due to differential RNA splicing of the heavy chain transcript. Hence (D) is correct.
Therefore, correct statements are (A), (C), and (D).