受講 and 受験: taking a course or sitting an exam
Compare attending an evening language course with a plan to take a school exam, identifying what the application and documents prepare for.
Learning through a course with 受講
受講 (じゅこう) refers to taking a course. The example 「春から夜間の語学講座を受講しています。」 is translated as “I have been taking an evening language course since spring.” The course has been attended since spring; this is more than the submission of an application.
The example 「受講を希望する人は申込書に名前を書いてください。」 is translated as “Those wishing to enroll should write their name on the application form.” The request addresses people who wish to enroll. It does not report that their applications or course attendance are complete.
Taking an examination with 受験
受験 (じゅけん) refers to taking an examination. The example 「来年は希望する学校を受験する予定だ。」 is translated as “I plan to take the entrance exam for my preferred school next year.” Read next year together with 予定: taking the exam is a plan.
The example 「受験に必要な書類を期限までにそろえた。」 is translated as “I gathered the documents needed for the examination by the deadline.” Gathering the required documents by the deadline is completed. Sitting or passing the exam is not stated.
Separate preparation from participation
受講 identifies participation in learning through a course, while 受験 identifies taking a test. Both can require applications or preparation, but those preparations do not erase the distinction between the activities.
Separate the ongoing course, the request to write a name, the planned school exam, and the completed document preparation. Attendance, examination participation, and passing are different facts to check.
What activities do 受講 and 受験 name in the evening-course sentence and the planned school-exam sentence?
Show the answer and why
受講 names learning by attending the course; 受験 names taking the school's examination. Course attendance is ongoing, whereas the examination is planned for next year. Preparing documents also does not establish that the exam was taken or passed.

