With this test you can test how much your students already know about a given subject or topic. You can use the results of this test to schedule your class. Which subjects need some extra attention. For the student this gives him or her some insights in which part of the class need some extra study hours.
This kind of test can be used to place the student in the appropriate class or level. For example for language classes this is often used prior to starting the class.
Progress or Achievement tests
These tests are used to measure progress in a given subject. This will mostly follow a diagnostic test or can be in regular intervals. If you measure regularly you get a better picture of the progress of your students.
These are internal tests given by the institution where the student is following classes.
Objective test have clear right or wrong answers. All multiple-choice test fall into this group. The students get a pre-defined set of answers to choose the correct answer from.
With this type of tests the maker of the exam has to pass judgement on the answers of the student. Mostly this in the form of free text questions or essays.
Read more about the difference between a test and an exam.