I will not speculate about what the author meant by "modeling", because within the realm of software it can mean different things. Perhaps you could use the comment box at the bottom of the article to ask him what he meant.
In the context of his article, I believe "prototyping" means building a mocked-up version of some aspect of a product for purposes of illustrating and testing an idea. For example, a paper prototype of a user interface might be a set of hand-drawn pictures that illustrate the essential nature of the user interface. Advocates of paper prototyping assert that testing the paper prototype will yield insights into the "real" product's requirements and design.
Done properly, prototyping can be a valuable tool for getting early input on a concept before investing a significant effort building an actual product.