I think graduate indicates only a university graduate in British English, but in American English can it perhaps also suggest a high-school graduate as well?
Could anyone tell me something about that?
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I speak AmE, but I have encountered the term school-leaver or school leaver in BrE and AuE writings.
Collins Dictionary defines school leaver:
School leavers are young people who have just left school, because they have completed their time there.
Cambridge Dictionary defines school-leaver:
a young person who is about to leave or has just left secondary school
We (UK) don't "graduate" from secondary (high) school as there is no simple pass or fail result.
However, the trend of "graduation" at all states of education is spreading in the UK.
Little Ladybirds nursery in Stockton-on-Tees in the North East of England has offered graduations since 2011. ... Kindergarten graduation has been an event in the US since at least the 1960s,
Do four-year-olds need a graduation ceremony? Justin Parkinson, BBC News Magazine, 23 July 2014
Scottish schools do, however, award a dux to one pupil (and maybe a semi-dux to a second) but this is not usually solely based on exam results.