According to StackOverflow, an entity-relationship model (ERM) is an abstract and conceptual representation of data, information aspects of a business domain or its process requirements. Ultimately ERM is being implemented in a database. A domain model is composed of the objects, behavior, relationships, and attributes that make up the industry that is the focus of development.
Both uses squares to model something, they have attributes inside and they have relationships between them. What's the difference, just the name?
Both are defined in ISO/IEC/IEEE 24765 : Systems and software engineering -- Vocabulary, as:
domain model "a product of domain analysis that provides a representation of the requirements of the domain."
entity-relationship diagram "a diagram that depicts a set of real-world entities and the logical relationships among them."
Furthermore, the standard notes that a domain model can represent are structure, information flow, functions, constraints and controls. In the UML those can be represented with class diagrams; as an example: structure with classes and associations, information flow using information flow items or information flow classifiers, operations, multiplicities, navigatabilities or multiplicities or OCL, and controls -- respectivly.