Sorry if this is elementary, but what is the difference between these two? Do they perform similar jobs or are they intended for different purposes?

The color.

But seriously, I think green putty is a bit smoother, but they both stink to high heaven. I much prefer using a two-part putty like Apoxie Sculpt. No stink, no harmful chemicals, no shrinkage, easier to use, etc., -- I cannot think of one thing I like about Squadron Green or White putties. They were all we had "back in the day," but there are much better products available now.