Here is a post, to compare and contrast the two styles of MVC I have worked with: Web application MVC and desktop application MVC. As I understand, the desktop application MVC came first and then we tried to fit that idea to Web applications.
To talk a bit about the architecture, the basic components of the two styles are the same: Model, View, Controller and hence the name. Sparing the details of the pattern itself, a subtle yet important difference between the two styles of MVC is that, for a desktop application all 3 components live in the same memory space on the same machine and this has some significant implications which we will talk about later. For a web application though, the controller and model live in the server memory space but the view partly lives on the server and partly on the client. The view is built on the server but interacted with on the client (through the browser).
Coming to the control flow, in a desktop application, the user interacts with the view to generate events. These events will be intercepted by a controller action which uses the model to update/retrieve data. There are multiple ways in which the view will be updated to reflect the model state change. Either the controller will directly update the view, or by employing the observer pattern. In the observer pattern, all the components interested in the model change, will register with the model. When the model changes, it informs all the observers of the change. This is the interesting bit of communication that you do not get to see in a web application. Since all 3 components, M,V and C, are objects in the same memory space, the communication between them is richer, hence a model can notify all the interested models/views about its changes. Another interesting pattern of communication is, the direct communication between the view and model on a user event. Given that the controller has bound the correct model action to a view event as a callback, the view can directly invoke the model action on the trigger of the event. Lets put this in perspective with an example. In the desktop trading application, lets say the user has the ability to change the trading currency. This currency is being used for transactions in multiple widgets/views on the same page. In MVC land, this currency change event is tied to some update action on the trading currency model. When the user changes the currency, the model is updated directly. The model then notifies all the registered observers (predominantly models) about the currency change who then subsequently update their respective views. This communication seems very natural in a desktop style MVC.
Lets look at the web application control flow. The user interacts with the view via the browser. The view is built on the server with 2 pieces of information: one, the actual view code and second, a mapping of user event to a controller action. Each user action is converted into an HTTP request by the browser. On the server side, the web application framework invokes the controller action. The controller action uses the model to retrieve/update data, builds the next view and sends it back to the browser as a HTTP response. The browser renders the view code and then the user is free to interact with the view again. In this style of communication, all the communication between the view and model has to be channeled through the controller. Going back to our example of updating trading currency, in a web application, updating the currency would mean having a currency update controller action that updates the necessary models and then builds the entire page with updates to all the necessary views and retaining the unchanged views. This seems like inelegant approach as opposed to the desktop style of MVC.