In most cases, if you are talking about cooking ingredients, physical objects or groups of people, they are the same. There are some instances in which they are different. If my method of doing something gets mixed result, it means that there are some positive and negative results. It is not completely positive. I would NOT say that I got combined results. If things are mixed up, it is an idiom meaning that they are confused. Again, you would not say "Things are combined up."

Combine：to bring into such close relationship as to obscure individual characters . Like :The two small shops combined to make a large one. Mix:to combine or blend into one mass ,hard to divide,but still keep individual characters. Like : Mixed nuts