DOM and SAX are both programming interfaces that can work with XML.
The DOM (Document Object Model) is a programming interface specification being developed by the World Wide Web Consortium (W3C) that lets a programmer create and modify HTML pages and XML documents as full-fledged program objects. DOM is a full-fledged object-oriented, complex but complete API, providing methods to manipulate the full XML document as a whole. DOM is designed for small XML trees manipulation.
The SAX (Simple API for XML) is a programming interface for XML, simpler than DOM. SAX is event-driven, streamed-data based, and designed for large trees.