As regards terminology of the 737 fleet, there seem to be a variety of options used.
Classic can refer to the steam-driven 100 and 200 series
737e is being used to mean the EFIS 300 - 500
and 737NG is the Next Generation as mentioned above.
Then there is the 737BBJ .......
My question would be why, if a Licence covers the 737 300 - 800 series, operators seem to insist on a NG course?