Difference between By a hair’s breadth and To a hair’s breadth

by a hair’s breadth —(also: by a fraction) by a very small degree or amount:

• If I swerve by a hair’s breadth from the straight line of the most rigid respectability, I’m done for.

to a hair’s breadth —(also: to a fraction) with great accuracy:

• You had plenty of time to put your heads together before the police arrived. I’m sure the stories would tally to a hair’s breadth.