Your sources of advice are correct when they say it is the domain model. In many instances, it will be quite closely aligned your data model as well.
Where the domain and data models differ is that the data model is relatively static in form (not content) whereas your domain model adds the specific constraints and rules of your domain. For example, in my data model (database) I represent blood pressure as smallints (systolic and diastolic). In my domain model, I have a "blood pressure reading" object that holds values for each of the two readings and that also imposes additional restrictions on the range of acceptable values (e.g. the range for systolic is much smaller than that for smallints). It also adds qualitative judgments on these values (a BP of 150/90 is "high").
The addition of these aspects of the problem domain is what makes the domain model more than just the data model. In some domains (e.g. those that would be better rendered with a fully object-oriented data model and that map poorly on the relational model) you'll find that the two diverge quite significantly. However, all the systems I've created feature a very high degree of overlap. Indeed, I often push a fair number of domain constraints into the data model itself via stored procedures, user-defined types, etc.