In MVP, the Presenter contains the UI business logic for the View. All invocations from the View delegate directly to Presenter. The Presenter is also decoupled directly from the View and talks to it through an interface. This is to allow mocking of the View in a unit test. One common attribute of MVP is that there has to be a lot of two-way dispatching. For example, when someone clicks the "Save" button, the event handler delegates to the Presenter's "OnSave" method. Once the save is completed, the Presenter will then call back the View through its interface so that the View can display that the save has completed.
MVP tends to be a very natural pattern for achieving separated presentation in Web Forms. The reason is that the View is always created first by the ASP.NET runtime. You can find out more about both variants.
Two primary variations
Passive View: The View is as dumb as possible and contains almost zero logic. The Presenter is a middle man that talks to the View and the Model. The View and Model are completely shielded from one another. The Model may raise events, but the Presenter subscribes to them for updating the View. In Passive View there is no direct data binding, instead the View exposes setter properties which the Presenter uses to set the data. All state is managed in the Presenter and not the View.
Pro: maximum testability surface; clean separation of the View and Model
Con: more work (for example all the setter properties) as you are doing all the data binding yourself.
Supervising Controller: The Presenter handles user gestures. The View binds to the Model directly through data binding. In this case it's the Presenter's job to pass off the Model to the View so that it can bind to it. The Presenter will also contain logic for gestures like pressing a button, navigation, etc.
Pro: by leveraging databinding the amount of code is reduced.
Con: there's less testable surface (because of data binding), and there's less encapsulation in the View since it talks directly to the Model.
In the MVC, the Controller is responsible for determining which View is displayed in response to any action including when the application loads. This differs from MVP where actions route through the View to the Presenter. In MVC, every action in the View correlates with a call to a Controller along with an action. In the web each action involves a call to a URL on the other side of which there is a Controller who responds. Once that Controller has completed its processing, it will return the correct View. The sequence continues in that manner throughout the life of the application:
Action in the View
-> Call to Controller
-> Controller Logic
-> Controller returns the View.
One other big difference about MVC is that the View does not directly bind to the Model. The view simply renders, and is completely stateless. In implementations of MVC the View usually will not have any logic in the code behind. This is contrary to MVP where it is absolutely necessary as if the View does not delegate to the Presenter, it will never get called.
One other pattern to look at is the Presentation Model pattern. In this pattern there is no Presenter. Instead the View binds directly to a Presentation Model. The Presentation Model is a Model crafted specifically for the View. This means this Model can expose properties that one would never put on a domain model as it would be a violation of separation-of-concerns. In this case, the Presentation Model binds to the domain model, and may subscribe to events coming from that Model. The View then subscribes to events coming from the Presentation Model and updates itself accordingly. The Presentation Model can expose commands which the view uses for invoking actions. The advantage of this approach is that you can essentially remove the code-behind altogether as the PM completely encapsulates all of the behaviour for the view. This pattern is a very strong candidate for use in WPF applications and is also called Model-View-ViewModel.