"a university student"
Yes, it is implied that a person attents a colledge, a university or an institute. We will accept that translation, just note that it is slightly off (студент университета HAS to study at the university; студент does not)
○ A note: in Russia, the word «колледж» (spread in recent decades) usually refers to an institution providing a focused practical education for some profession rather than a wide range of skills and/or knowledge a university does. For example, a scientist who studies old Persian poetry usually comes from a university. It is different from the U.S. usage.
Some colleges take students who only have 9 years of school education and a curriculum might be as short as 1 or 2 years long (though, people coming from the 9th grade typically have longer programs and are taught some of the material they missed having left school 2 years earlier than they might have).