A machine learning model is a file that has been trained to recognize certain types of patterns. You train a model over a set of data, providing it with an algorithm that it can use to reason over and learn from those data.
A model parameter is a configuration variable that is internal to the model and whose value can be estimated from the given data. They are required by the model when making predictions. Their values define the skill of the model on your problem.
Some examples of model parameters include: The weights in an artificial neural network. The support vectors in a support vector machine. The coefficients in linear regression or logistic regression.