People say midterm or midterm exam. Nobody says midterm test, although it makes sense literally.

Midterm exam is better, since it is usually a 'bigger' cumulative test, testing material from the beginning of the semester till the middle of the semester. Still, most people just say, "Midterm" student: When is the midterm? teacher: Midterms are mid-May.

Test is a less not so serious exam, you can have both during the midterm but habitually during the midterms, the marks are quite important so we used the term exam