She sounds as though she knows taking the exam makes her a commander by rank.
Yeah, emphasis on the pronoun. Taking the same exam might make Nurse Ogawa a Lieutenant (j.g.), or Captain M'Benga a Commodore.
However, It also was made to sound like Dr. Crusher had undergone the same promotion, lt. cmdr to cmdr upon completion of the bridge officer's exam
This makes me think that something weird is going on, or there is a common occurrence of this nature, where medical officers aboard starships often don't rise above the lt. cmdr. rank unless they get compensatorily promoted after completing bridge officer testing
Perhaps the only way for a medical officer to achieve higher ranks is to serve in medical facilities. This would mean Beverly had always held bridge officer qualifications her entire time aboard the Enterprise