The separation of concerns that’s quoted as being an advantage of MVC is actually also an advance of a 3-layer/3-tier system. There too, the business logic is independent and can be used from different presentation tiers.
A main difference is that in classic MVC the model can have a reference back to the view. This means when data is updated the model can push this data back to possibly multiple views. The prime example is a desktop application where data is visualized in multiple ways. This can be as simple as a table and graph. A change in the table (which is a change in one view) is first pushed via the controller to the model, which then pushes it back to the graph (the other view). The graph then updates itself.
Since desktop development is on the decline, a lot of programmers have only come in touch with MVC in some web variant, e.g. via JSF in Java EE.
In those cases the model almost never has a reference to the view. This is because the web is mainly request/response based and after a request has been served, the server cannot send additional information. I.e. an update pushed from the model to the client would be meaningless. With reverse ajax/comet this is changing, but many web based MVC frameworks still don’t fully utilize this.
Thus, in the case of web based MVC, the typical “triangle” between M, V and C is less there and that MVC variant is actually closer to an n-tier model than ‘true’ MVC is.
Also note that some web MVC frameworks have an intermediate plumbing part between M, V and C called a backing bean (Java/JSF) or code behind (ASP.NET). In JSF the controller is provided by the framework, and the view often doesn’t bind directly to the model but uses this backing bean as an intermediary. The backing bean is very slim and basically just pre-fetches data from the model one way and translates model specific messages (e.g. exceptions) into view specific messages (e.g. some human readable text).