I think it's important to provide some clarity here for posterity.
A data model is a design for how to structure and represent information. By structure, I mean concerns like "fifth normal form". By representation, I mean choosing a computer serialization, such as integer, floating point, or string.
The term domain model actually has two conflated meanings.
- A model of essential characteristics of real or imaginary things in the world. In this kind of model, classes represent human conceptualizations and instances are things in the world. For example, a "Person" class would have instances including you and me, and an essential characteristic might be that every Person has a mother. This kind of model is often called an conceptual ontology or concept model and is intended to provide meaning.
- A model of required information about things in the world, usually with some system in mind. In this kind of model, classes represent information that must be stored about things in the world. For example, a "Person" class would have instances representing required information about you and me, such as first name, last name, date of birth, current height, and current weight. This information often does not include all essential characteristics, such as our mothers, because, for the purposes of a particular system, that information is not required. This kind of model is often called an information model, conceptual data model, or operational ontology.
Both the UML and OWL languages can be used to represent either kind of domain model. Both can be considered analysis models, as they are used to analyze a domain. One is used to understand things in a domain, the other is used to gather requirements to build a particular software or database system for things in a domain. Both are necessary, and, unfortunately, they are usually conflated such that people building an analysis model are themselves confused about what they are modeling!