Conceptual Vs Data Vs Domain model

I'm trying to change the mindset of my data model design to design a Catalog, Products and Category domain model.
 

 The conceptual model:  
 

 Catalog contains Products belonging to a Category.
 

 Data Model:
 

 Table Catalog
 [
 CatalogID
 ]
 

 Table Product
 [
 CatalogID (Catalog.CatalogID Foreign Key)
 CategoryID (Category.CategoryID Foreign Key)
 ]
 

 Table Category
 [
 CategoryID
 ]
 

 Domain Model:
 

 The domain model (class model) can be modeled in two ways as following. Thinking about the aggregate root, the Catalog can be an aggregate root.
 

 To me the Model 1 resembles a data model when the Model 2 resembles an aggregate root.
 

 What do you think?
 

 Model 1: 
 

 class Catalog
 {
 List<Product> Products;
 }
 

 class Product
 {
 Category Category;
 }
 

 class Category
 {
 }
 

 Model 2:
 

 class Catalog
 {
 List<Category> Categories;
 }
 

 class Category
 {
 List<Product> products;
 }
 

 class Product
 {
 }