When you choose a mission for a class, all the students currently in that class will receive a notification at the top right of their screen inviting them to start that mission.
Currently, it’s not possible to recommend different missions to different students in the same class. However, any student can change their mission at any time by opening the "Subjects" menu and choosing a mission.
If you're using Khan Academy's coach reports, you might find it helpful to divide your students into classes based on the missions they’re working on (e.g., one class for all the students working on Algebra I, another for all the students working on Geometry, etc.). That way, when you look at coach reports for any class, the filter will default to the mission associated with that class. If you want to see all students on the same report, you can set the class filter on the report to "All students."