EAI (Enterprise Application Integration) is a methodology for integrating multiple organizational applications. At the same time, SOA (Service-Oriented Architecture) is an architectural approach for building applications using a collection of loosely coupled, reusable services. ESB (Enterprise Service Bus) is a software architecture that implements the principles of SOA, providing a middleware layer for integrating applications and services. In short, EAI is a methodology, SOA is an architecture, and ESB is a software solution that implements SOA principles.