Monoclonal and polyclonal antibodies are produced through different processes. Monoclonal antibodies are derived from a single clone and recognize a single epitope, while polyclonal antibodies recognize multiple epitopes. Monoclonal antibodies are produced through hybridoma technology involving immunizing an animal, fusing lymphocytes with myeloma cells, and screening for antibody-producing clones. Polyclonal antibodies involve immunizing an animal and purifying the antibody response. Both have applications in research, diagnosis, and therapy due to their specific binding abilities.