I think it would be fair to say that people who take Approach 1 are engaging in a lot of confirmation bias, but that's a much more general term and doesn't really describe the approach.

Anyway, my question is, do Approach 1 and Approach 2 have generally or somewhat understood shorthand names or, if you want to explain to a bystander what these are, do you have to actually describe the behaviors as I did above? 

 @ed709062 1. resolving cognitive dissonance.  2, critical thinking

For cognitive dissonance, the brain takes the most efficient path to resolve the uncomfortable emotion, then stops.