An interface is a specification for methods that a class must implement, while an abstract class can contain both implemented and non-implemented methods. The main differences are that interface methods are implicitly abstract, variables in interfaces are final by default, and interfaces can only extend other interfaces while abstract classes can extend classes and implement interfaces. Exception handling in Java uses try/catch blocks to handle exceptions, with checked exceptions requiring handling at compile time. Abstract classes are incomplete classes that cannot be instantiated directly but can serve as base classes, while object adapters use delegation to adapt existing classes to new interfaces. Sockets in Java allow reading/writing between client and server programs, with the server creating a ServerSocket to listen for client connections.