Difference between Second Thought and Rethink

SECOND THOUGHT vs RETHINK: NOUN

(transitive; intransitive verb) To reconsider (something) or to involve oneself in reconsideration.

Football team, Come off, Hockey player, Call up, Fall short, Baseball team, Bring on, Michael jordan, Basketball player, Come through, Look to, Free agent, Reconsideration, Rethink, Afterthought

Rearrange, Revise, Reshape, Ponder, Redefine, Consider, Revisit, Reappraise, Reexamine, Reevaluate, Reconsider, Reassess, Second thought, Afterthought, Reconsideration

Basketball team, Baseball player, Football team, Come off, Hockey player, Call up, Fall short, Baseball team, Bring on, Basketball player, Come through, Look to, Free agent, Reconsideration, Afterthought

Contemplate, Refocus, Rearrange, Revise, Reshape, Ponder, Redefine, Consider, Revisit, Reappraise, Reexamine, Reconsider, Reassess, Afterthought, Reconsideration

So, on second thought, you should probably fret.
Zionism after the Holocaust without a second thought.
The second thought is that grievance justifies violence.
He also granted favours without a second thought.
So, without a second thought, I purchased it.
Definitely, you should never give a second thought.
On second thought I take that one back.
My first thought was "Who allowed them to do that?" and my second thought was "I can't wait to do that.".
First thought was, where did immigration get my email address, second thought was why is this the first time I'm hearing about this?.
Trinity is so clearly contrary to any rational thought as not to warrant a second thought from sensible people.