Beliefs

Simply, a belief defines an idea or principle which we judge to be true. When we stop to think about it, functionally this is no small thing: lives are routinely sacrificed and saved based simply on what people believe. Our brains become intimately emotionally entangled with ideas we come to believe are true and emotionally allergic to ideas we believe to be false. They can help us having faith on something but it can also affect or professional life if we believe that something we should do on our current work is wrong. This leads to the rather ironic conclusion that infants and animals are actually better at reasoning from evidence than adults.

Sources: https://www.psychologytoday.com/blog/happiness-in-world/201104/the-two-kinds-belief

Mental Model

"Mental Model is a term that is used to explain an individual’s personal thought processes about how the world works."

Beliefs, ideas, images and verbal descriptions that we consciously or unconsciously form from our experiences. Basically it's what makes the shape of our mind, it changes our opinion, our way of seeing things and many other stuff.

An example:

 

If the organism carries a ""small-scale model"" of external reality and of its own possible actions within its head, it is able to try out various alternatives, conclude which is the best of them, react to future situations before they arise, utilize the knowledge of the past events in dealing with the present and future, and in every way to react in a much fuller, safer, and more competent manner to the emergencies which face it.
- Kenneth Craik, a Scottish psychologist, 1943

Sources: http://www.createadvantage.com/glossary/mental-model

 http://www.alleydog.com/glossary/definition.php?term=Mental%20Model#ixzz497tODSh3