Let's take the example "I am going to the movies" and "I will go to the movies." They are both referring to future events. "I am going . . . is often followed by a definite time. For example - "I am going to the movies tonight," or "I am going to the doctor on Wednesday." If someone does not include the definite time information, and just says "I am going to the movies," or "I am going to the store," you can picture them walking out the door and assume it is happening immediately.
With "I will," you can also follow it with a definite time, such as "I will brush my teeth tonight" or "I will do my homework at 7:00 pm." If "I will" is just left open-ended, with no definite time information, it means something that you intend to do in the future, but not necessarily immediately (and it may or may not happen). An example is "I will go to the doctor if I don't feel better soon" or "I will learn how to speak French."