In Domain-Driven Design (DDD), an application service is a service that operates at the application layer, and provides a set of actions that can be performed by the application to implement use cases or features that involve multiple aggregates or entities from the domain layer. The application service is the public API of the application, and is responsible for coordinating the interactions between the user interface, the domain layer, and any infrastructure or external systems.

A domain service, on the other hand, is a service that operates at the domain layer, and provides a set of operations or behaviors that cannot be expressed by a single entity or aggregate in the domain. Domain services are used to encapsulate complex business logic or behavior that spans multiple entities or aggregates, and that cannot be naturally expressed as part of the state or behavior of an aggregate root.

The distinction between application services and domain services is important because it allows you to separate the coordination and presentation concerns of the application from the core domain logic and behavior. This helps to keep the domain model clean, expressive, and maintainable, and to ensure that the application is flexible and adaptable to changes in the domain over time.