Not only the mainstream magazines, but also some experienced practitioners and even scholars use the term business model and strategy interchangeably. Well, that's NOT quite right!
The below video by Harvard Business Review explains the difference in a very straight forward term.
Source: Harvard Business Review, 5th Aug 2016
Further to this, two great articles from HBR helps to understand the difference between strategy and business model.
Micheal Porter in his "What Is Strategy? " published in 1996 explains that: "the essence of strategy is choosing to perform activities differently than rivals do". He discussed that strategy is a matter of working out your company’s best position relative not just to pricing pressures from rivals but to all the forces in your competitive environment.
Different to the above definition, is the definition of business model. In her great and very well articulated article "Why Business Models Matter" published in 2002, Joan Magretta explained that: “Business models are, at heart, stories—stories that explain how enterprises work. A good business model answers Peter Drucker’s age-old questions: Who is the customer? And what does the customer value? It also answers the fundamental questions every manager must ask: How do we make money in this business? What is the underlying economic logic that explains how we can deliver value to customers at an appropriate cost?".
Some may say that addressing these questions could explain the firm’s strategy, which suggests that business models and strategy are conceptually very similar. But Magretta goes on to say: “... but a business model isn’t the same thing as strategy, even though many people use the terms interchangeably today. Business models describe, as a system, how the pieces of a business fit together. But they don’t factor in one critical dimension of performance: competition. Sooner or later—and it is usually sooner—every enterprise runs into competitors. Dealing with that reality is strategy’s job... A competitive strategy explains how you will do better than your rivals.” (p.94)
So a firm’s strategy is specific to that firm and that firm alone. By contrast, a business model can be conceived as an activity system, which explains what the key activities are and how they are connected.
“Today, “business model” and “strategy” are among the most sloppily used terms in business; they are often stretched to mean everything and end up meaning nothing. But as the experience of companies like Dell and Wal-Mart show, these are concepts of enormous practical value.” (Magretta 2002)
“The definition of a business model is murky at best. Most often, it seems to refer to a loose conception of how a company does business and generates revenue. Yet simply having a business model is an exceedingly low bar to set for building a company. Generating revenue is a far cry from creating economic value ...” (Porter 2001, p.73)
Magretta, J. (2002) Why Business Models Matter, Harvard Business Review, May, pp. 86-92.
Porter, M. E. (1996), What is strategy? Harvard Business Review, November-December.
Porter, M. E. (2001), Strategy and the Internet, Harvard Business Review, March, pp. 63-78.