入門 and 入学: introductory learning and school entry
Compare an introductory pottery course and a statistics book with entry into middle school or university. Identify a beginner learning level separately from enrollment in a school.
A starting level and entry into a school
入門 (にゅうもん) concerns an introduction or beginner's guide, while 入学 (にゅうがく) concerns school admission or enrollment. Identify a starting learning level or resource separately from entering a school as a student.
Reading an introductory book and becoming a school student have different roles. The shared character 入 does not make them the same admission procedure, and signing up for a beginner course does not establish mastery or completion.
A beginner course and an introductory book
「初心者向けの陶芸入門講座に申し込んだ。」 — “I signed up for an introductory pottery class for beginners.” The course is introductory pottery for beginners. 入門 identifies its starting level, and 申し込んだ reports registration rather than completed attendance.
「この本は統計学への入門にちょうどよい。」 — “This book is perfect as an introduction to statistics.” The book is evaluated as suitable for beginning statistics. Its introductory role does not report complete acquisition of statistics or entry into a school.
The school entered and a lifestyle change
「弟は春から近くの中学校に入学する。」 — “My younger brother will enter the nearby middle school in the spring.” The stated future school is a nearby middle school. 入学する concerns entering that school from spring, rather than identifying a beginner learning level.
「大学への入学を機に、一人暮らしを始めた。」 — “I began living on my own when I entered university.” University entry is the occasion for beginning to live independently. Read that entry and lifestyle change separately from the introductory-course and book examples.
What do 入門 in the statistics-book example and 入学 into university identify: a resource's learning level or entry into a school?
Show the answer and why
入門 identifies the book as suitable for beginning statistics. 入学 identifies entering a school as a student. Reading an introductory book does not establish university enrollment or student status.

