Advancing an exponent 1-4 skill requires a number of routine tests equal to the exponent. Also, for exponent 1-4, a character needs difficult tests equal to half the exponent, or challenging tests equal to his exponent divided by three (rounded up).
Exponent 1-4 skills must be advanced by filling up the routine test requirement. Then, meeting either the difficult or challenging test requirement will push the skill to the next exponent level.
The former excerpt doesn't seem to require that the difficult/challenging tests take place chronologically following the routine tests, but the latter excerpt does. Which is it?