you are talking about relation, in this context fk is an abstract concept

linked article describes fk as an dbms construct - a schema constraint

relations and conceptual foreign keys may exist without dmbs constraints, in such scenario dmbs does not guard validity of conceptual "foreign keys" and treats them as usual data

for example consider schema:

user{id,name}; book{id,title}; library_borrow{id,user_id,book_id,date}

if you want you may define a constraint:

ALTER TABLE library_borrow ADD CONSTRAINT FOREIGN KEY (user_id) REFERENCES user(id) CONSTRAINT fk_library_borrow_user_id;

if you do not define such constraint then dbms will not verify existence of records in `user` table when you insert data in library_borrow

absence of constraints affects also indexes - if you do not define a constraint you usually have to manually define an index on fk column