Is the Controller in MVC considered an application service for DDD?

The application layer is somewhere between the domain layer and the presentation layer. The controller is part of the presentation layer, sends commands or queries to the application layer, where the application services execute them using the services and objects of the domain model. So controllers are different from the application services, and they are probably bound to the actual communication form, e.g. HTTP. You should not call domain services from controllers directly, this might be a sign of misplaced code.

Domain Driven Design: Domain Service, Application Service

• Domain Services : Encapsulates business logic that doesn't naturally fit within a domain object, and are NOT typical CRUD operations - those would belong to a Repository.
• Application Services : Used by external consumers to talk to your system (think Web Services). If consumers need access to CRUD operations, they would be exposed here.

So your service is probably an application service and not a domain service, or some part app services, some part domain service. You should check and refactor your code. I guess after 4 years this does not matter, but I had the same thoughts by an application I am currently developing. This app might be too small to use DDD on it, so confusing controllers with app services is a sign of overengineering here.

It is an interesting question when to start add more layers. I think every app should start with some kind of domain model and adapters to connect to that domain model. So if the app is simple enough, adding more than 2 layers might be not necessary. But that's just a thought, I am not that experienced with DDD.

The controller is not considered a service in DDD. The controllers operate in the UI tier. The application services gets data from the DB, validates data, passes data to client (MVC could be a client but so could a request coming from a winforms app) etc etc.

All the controller is doing is servicing requests from the UI. Its not part of the application domain.

A Layered Architecture splits the application up into UI-Layer, App-Layer, Domain Layer and Infrastructure Layer (Vaugn Vernons Implementing Domain-Driven Design (location 2901)). The controller falls in "Application Layer" of this broader design architecture and will therefore interact directly with the domain services in the model and is considered an application service. Not only that, it'll will obviously also use the entities and aggregates as available.