In the US, University is widely known as “College” in regards to undergraduate studies. The word “University” can refer to the same institute, but it is mostly used for graduate studies.
American schools have specific terms for students in each year of high school:
K-12 ia an expression that indicates the range of years of supported primary and secondary education found in the United States
Freshman for a student currently in Grade 9 (Year 10 in UK)
Sophomore for a student currently in Grade 10 (Year 11 in UK)
Junior for a student currently in Grade 11 (Year 12 in UK)
Senior for a student currently in Grade 12 (Year 13 in UK)
When referring to students who have just completed a grade in high school, and are about to start another grade at the end of summer, the word “Rising” is used. For example, a rising sophomore is someone who completed Grade 9, and will enroll in Grade 10 (their Sophomore year) starting the autumn.