No, the ORM is the thing that maps a code-based model to your database and vice versa.
For basic CRUD apps, where your model in code is literally just DTOs that represent the database and you're loading, editing, and saving them, that's how you'd use it. If you do have a "proper" Domain Model, then it's a bit more complex because ideally you'd want to decouple the shape of the Domain Model classes from the shape of the database tables.
To elaborate, you would create your model in your code to represent the Domain Model (i.e. the various elements of your problem domain), build some sort of "memento" classes that are pure DTOs that you can convert your Domain Model classes from/into. Then configure an ORM (object relational mapper) to map those memento DTOs to a database. I.e. Generate SQL statements that will update the database based on the model objects you give to it.
I can understand some confusion, because there are tools (LINQ to SQL being one) that actually generate model classes in a designer for you. This isn't pure ORM, like NHibernate, where you provide the ORM plain old objects and some mapping configuration that it uses (often in conjunction with reflection) to automatically generate the SQL statements for the database. You could possibly get away with using EF Code First to map a Domain Model directly to the database, but I think in the end it may get messy as you try to make changes to one or the other.