What are the different titles for grade school and university students ?

Grade schools have grades to describe the different levels. (Plus Kindergarten for the level before grading.)

Colleges and Universities use the same descriptions as high schools: Freshman, Sophomore, Junior, Senior. Each describes a year in a standard four year curriculum.

They are descriptors, they don’t carry any meaning beyond that.

Kindergarten, elementary, Middle School, High School further separated into freshman, sophomore, junior, senior.

Different school systems have different descriptors. In the school district where I grew up, there was kindergarten, grade school (grades 1–8) and high school (freshman, sophomore, junior and senior). In the school district a few miles away, there was kindergarten, primary (grades 1–5), junior high school (grades 6–9) and senior high (grades 10–12). In the district here, most schools are either elementary (1–5), junior high (6–8) and high school (9–12). However, there are some concept schools that are designated P-20, which indicates a comprehensive education package all the way from pre-school (pre-kindergarten) on up to high school and college grad student level.