Bias referes to a tendency to believe that some people, ideas, etc., are better than others, which usually results in treating some people unfairly. When evaluating sources, it is important to look for and recognize bias so as not to confuse a writer's opinion with facts. It is equally important to be aware of your own biases so that you don't discount credible sources just because they differ from your opinions.
Fallacies are arguments that comes to a conclusion without evidence to support them, and they come in many varieties.