BA 737 pilots are nearly all 'dual' rated on the 737. The -200 is a separate rating. Once you get the -400 rating (from the CAA) it also qualifies you to fly the 300,500,600,700 and 800.
Within BA there are 200, 300, 400 and 500 series a/c. There are even some differences between the different types of -400. i.e.-4Q8,-436,-4SQ. However the CAA seem to be happy with this situation!!!