J2EE Patterns are a set of design patterns for software development using the Java programming language. These patterns provide solutions to common problems that arise in J2EE-based software development, such as implementing security, managing transactions, and integrating with other systems.

Interpreter pattern is a design pattern that implements a specialized language, allowing the client to express complex operations in a simplified manner. The pattern involves creating an interpreter class that evaluates expressions in the language, and performs the operations specified by the expressions. This pattern can be useful in situations where you want to allow the client to specify complex operations in a concise and easily understandable manner.

The Front Controller pattern provides a centralized request handling mechanism, while the Intercepting Filter pattern provides a way to intercept and modify incoming requests before they are processed by the target resource.

Repository Pattern is used to abstract data access and encapsulate the underlying data storage, making it easier to change data storage solutions without affecting the rest of the application. It also helps to manage the complexity of a software system by providing a clear separation of concerns between the data access logic and the business logic.

The Transfer Object pattern involves a simple object used to pass data between layers, while the Data Access Object pattern involves an object used to perform CRUD operations on a database.

The Service Locator pattern is used to maintain a centralized registry of service objects, and provides a single point of access for clients to access the services through a locator object.

Decorator pattern is a design pattern that allows objects to be decorated with additional responsibilities, dynamically, at runtime. The pattern involves creating a decorator class that wraps the original object, adding the new responsibilities to the original object's behavior. This pattern can be useful in situations where you want to add or remove responsibilities from objects dynamically, without affecting the behavior of the original objects.

Design Patterns are usually categorized into three types: Creational, Structural, and Behavioral. Creational patterns deal with object creation mechanisms, trying to create objects in a manner suitable to the situation. Structural patterns deal with object composition, creating relationships between objects to form larger structures. Behavioral patterns focus on communication between objects, what goes on between objects and how they operate together.

CQRS and Event Sourcing are separate patterns and can be used independently of each other. However, using Event Sourcing with CQRS can provide benefits in terms of versioning and auditing.

A Static class is a class that cannot be instantiated and can only have static members. It is a sealed class, which means it cannot be inherited. A Singleton class is a design pattern that ensures a class has only one instance while providing a global point of access to this instance. It uses a private constructor and a static instance variable to ensure that only one instance can be created. Unlike a Static class, a Singleton class can have both static and instance members.

The State pattern is a design pattern in which an object, called the context, holds a reference to an instance of one of several possible concrete state objects, each of which represents a distinct state of the context and implements a common state interface. The State pattern allows the context's behavior to be altered dynamically by changing its state. The State pattern is used to implement state machines, allowing an object's behavior to be altered as its internal state changes.

The choice between Repository Pattern and "smart" business objects depends on the specific requirements of the project, but in general the Repository Pattern provides better separation of concerns and a common interface for data access.