"Graduating"

In SCotland I believe it may still be called matriculation, but that hasn't existed in England & Wales for many decades. There is no word used for a person who leaves (high) school, whether to go on to college/university, to work, or otherwise. Just "school leaver". "Matriculation" did not refer to leaving school, but to the final exam that one took at school. In E&W that was long ago replaced by the General Certificate of Education, known as the GCE. There were/are two levels - Ordinary ("O") level was taken at around the age of 16 (variable) and generally covered up to 9 or 10 subjects. Advanced ("A") level is a further two years later and covers fewer subjects in greater depth - generally in the Arts it was 3 subjects and in the Sciences 4, though again these varied. In recent years the whole process has been dunned down and changed frequently, and I am out of touch.

The closest I am to the UK education system (remembering that Scotland is different from E&W) is that Amanda Syme's younger daughter (Christine) is presently at school in Scotland. Amanda ("Sunshine") may be able to add some clarification.

The terms "high school" and "grade school", particularly the latter, are American terms not generally recognised in the UK. To us it's just school, whether primary or secondary. And the term "school' in the UK only applies to that phase of education - colleges and universities are never called "school". Perversely though, individual teaching segments of universities may be called "school". I attended a "school of mathematics" at my university, and in London as (I believe) part of London University there is the "School of Tropical medicine".