CoC means a developer only needs to specify unconventional aspects of the application. For example, if there is a class Sale in the model, the corresponding table in the database is called sales by default. It is only if one deviates from this convention, such as calling the table "products sold", that the developer needs to write code regarding these names. Generally, this leads to less code and less repetition.
DRY means that information is located in a single, unambiguous place. For example, using the ActiveRecord module of Rails, the developer does not need to specify database column names in class definitions. Instead, Ruby on Rails can retrieve this information from the database based on the class name.