You will, however, go through differences training prior to being qualified on the NG or vice versa.
The 737 is not alone in this regard. I, for one, hold a CL-65 type which is common for all CRJs but needed to go through differences training when going from the -200 to the 700/900. I also hold an ERJ-170/190 type rating and am currently qualified in the -170 and the -175. I will need differences training to transition to the -190.