Am I correctly concluding that these two AC/DC adapters are interchangeable
You already comprehended that the current delivering capabilities of the "lighter" one are basically double the heavy one.

It is doubtful that you will get the same type of outputs from both of these in terms of voltage over various amounts of load current. The "heavy" one is a simple transformer wall wart with a diode bridge rectifier and maybe a filter capacitor. At small to no load this heavy one will most likely be outputting a voltage that is nearly half again as much as 12V. As load is increased up to the rated 1A the average voltage will come closer to 12V but the output will also be pulsing with ripple at 60Hz. 

The "light" unit will tend to have a much smoother output voltage and less ripple effect. Such ripple will, if any, be at a much higher frequency matching the switching frequency of the energy converter inside. There will also be an output much closer to the rated voltage at no load and staying fairly close to that level as the load is increased up to the maximum 2A level. 

Compatibility between these two will depend on:


Actual current load
Tolerance of the load to voltage level
How the load deals with noise and ripple
If the connector ends are same size and polarity