Sex is an anatomical determination dictated by genetics and developmental processes. The condition of intersex demonstrates that sex is nonbinary.

Gender is a social construction assigned to expressions in fashion, career goals, hobbies and entertainment preferences, etc.

The phrase "girl who identify as a boy" seems deliberatly constructed to attack the notion of choice in gender expression,or supremacize anatomical or genetic determination over social construction. But in the great majority if situations, it's more meaningful to respect the person's chisen gender identity without regard to how that aligns with their genes or anatony. If someone with a penis is more comfortable identifying as a girl, it hurts no one to just call them a girl.

"Tomboy" describes a girl whose fashion choices and hobbies tend more toward those traditionally associated with masculinity, but without identifying as a boy per se. It's a culturally loaded idiom that reinforces binary gender notions.