The under 250 grams rule allows you to operate the drone without a registration of the operator with the FAA and getting a registration number that must be applied to the drone. It does not exempt you from following the drone operating rules (<400AGL, VLOS, prohibited areas, etc.).
If you have an airman certificate from the FAA for some other operation, they have more clout over you than a "regular" operator. Your certificate can be revoked if you are caught violating the drone rules. They can argue that you exhibit poor judgement.
Every recreational operator is also supposed to take "The Recreational UAS Safety Test" which teaches the rules.
https://www.faa.gov/uas/recreational_fliers/knowledge_test_updates/