While a mental model is a person's idea of what something should look like or how it should work, a conceptual model is the actual product or idea that the designer has created.
Slide 3
Successful Use of Conceptual Models
Take the time to purposely create the design around your user's mental model. Don't simply design around the existing technology.
Understand that if you have a product that isn't familiar to your user, you will need to offer some form of training to help bring them up to speed so that they can successfully develop a new mental model around their experience.