By the way - with reference to data modelling I\'m referring to logical or conceptual data models - not physical ones.
The question came up during a discussion at wo
Domain Modeling (in the sense of Domain Driven Design) is all about modelling the behavior of the domain concepts, while Data Modeling focuses mainly on... data.
It doesn't mean that Domain Modeling ignores data structures. It just puts more emphasis on operations and how they can be uses to solve problems.
I don't know much about other than Domain Driven Design domain modelling techniques, but DDD involves (apart from modeling data and behavior) also explicit modelling of consistency boundaries (aggregates).
This is an old thread, but here's a slightly improved answer to clarify some of the others posted here.
The concept of 'domain' (and other kinds of models such as conceptual, logical and physical) is orthogonal to the technique used to represent the model (eg. ERD, UML etc). A domain model is essentially the same as a conceptual model, but different design methodologies might have slightly different terms and definitions. While it's common to draw domain models using UML or ERD to describe entities and their relationships (or classes/methods in UML), this only applies to modelling the information to be managed by a system - logically, the concept of domain modelling (or conceptual modelling, logical modelling or physical modelling, etc) can apply to any problem situation and a solution. Depending on the nature of the problem and the problem solving approach, other modelling techniques could be used to achieve the same goal.
In short, domain modelling and conceptual modelling are essentially the same thing, hair-splitting definitions aside. The concept applies to what the modeller is trying to communicate. The concept of data modelling (ie. ERD) or object-oriented modelling (ie. UML) refers to how the modeller communicates it.
I would say that a domain model describes the problems (what we want to manage/solve) on a given domain. The data model would describe the solution (how we're going to solve it) to the problem described on the domain model.
However, we are indeed in murky waters...
Good question, the problem is that it depends on the definion of the terms, I think they differ slightly based on the sources. I would agree with previous answer - domain models are for describing the problem domain, at least the part you need to develop a solution. You describe all the various entities, their relations and their behaviour. I think that this is also the view from the Domain Driven design perspective. Data models on the other hand are used for describing the data in your system and relations or associations between them. This is useful for describing what needs to be stored in the system and might also give hints how. I think data models would apply for your "no operations" rule, because they are not important in this respect.