The difference is that an anemic model separates logic from data. The logic is often placed in classes named **Service, **Util, **Manager, **Helper and so on. These classes implement the data interpretation logic and therefore take the data model as an argument. E.g.
public BigDecimal calculateTotal(Order order){
...
}
while the rich domain approach inverses this by placing the data interpretation logic into the rich domain model. Thus it puts logic and data together and a rich domain model would look like this:
order.getTotal();
This has a big impact on object consistency. Since the data interpretation logic wraps the data (data can only be accessed through object methods) the methods can react to state changes of other data -> This is what we call behavior.
In an anemic model the data models can not guarantee that they are in a legal state while in a rich domain model they can. A rich domain model applies OO principles like encapsulation, information hiding and bringing data and logic together and therefore a anemic model is an anti pattern from an OO perspective.
For a deeper insight take a look at my blog https://www.link-intersystems.com/blog/2011/10/01/anemic-vs-rich-domain-models/