I would say just as a general rule, e.g. in news broadcasting, to define the category,
sport BE = sports AE
Even in the plural, it takes a singular verb, like physics or ethics.
In AE, the singular is only the countable form, like 'What's your favorite sport?' or 'Children who play a sport are less likely to be overweight.'
In school in the US, 'sports' usually refers to team sports, which are considered extracurricular activities, with practice usually after school in the afternoons.
The for-credit class that is required for health and fitness during the school day (in the earlier grades, in my day, up to about grade 9 or 10) is usually called PE or gym, interchangeably, but not sports.
mistress / master BE = teacher AE
headmaster / headmistress / head teacher BE = principal AE
The woman who taught girls' PE was the PE teacher, though she was also often a coach of something or other, maybe tennis. Boys' PE was taught by a male coach (of football, basketball, baseball, or in lower grades all three), who was always called 'coach' rather than 'teacher,' because 'coach' is the most exalted title (and the most highly-paid job apart from maybe the principal) that one can have in an American school. /-;