A bijective function (also called isomorphic) is a one-to-one mapping between the persons and the bikes (between the domain and codomain). That's the assertion

A bijective function (also called isomorphic) is a one-to-one mapping between the persons and the bikes (between the domain and codomain). That's the assertion made in the article - that a bijection and an isomorphism are the same thing. That's just not correct, and the distinction matters in general, even if you have not yet encountered a situation where it caused a problem. If you care only about the bijective property, why bring isomorphism into it?