図書館 and 書店: activities at libraries and bookshops
Distinguish a facility for using books from a shop for buying them.
Using a library
図書館 (としょかん) means library. 「図書館で本を借りました」 means borrowing a book at a library.
「借りた本を図書館に返しました」 means returning the borrowed book to the library. で marks the borrowing location, while に marks the return destination.
Choosing at a bookshop
書店 (しょてん) means bookshop. 「書店で辞書を買いました」 says a dictionary was bought at a bookshop.
「書店に入りましたが、何も買いませんでした」 says the speaker entered but bought nothing. Entry and purchase are separate.
Visit versus result
「図書館で読みましたが、借りてはいません」 says the book was read at the library but not borrowed. Reading and checking out are distinct.
「書店に本を注文しました」 means ordering a book from a bookshop. It does not establish receipt.
Does entering a bookshop necessarily mean buying a book?
Show the answer and why
No. Visiting and purchasing are separate facts.