I tend to think of a specialist as anyone who focuses on a certain discipline, whatever field they're engaged in. A highly-trained specialist would be someone who has not only chosen a specific discipline, but one who's also spent time perfecting their skills within that discipline.

Another way of saying it would be to call someone who has started training in Kung-fu as a martial arts specialist, and calling a Kung-fu Senpai a highly-trained specialist.

Of course, in Saf's case I'm still wrong, since she's not really had any extensive training in close-combat compared to any other military officer, but she has had extensive battlefield experience in its use and tactics, which would make her more of a veteran specialist rather than just a highly-trained specialist.