"Heading to" is specifically describing the direction of movement. "Going to" be used that way, but it could also be used to describe a regular or habitual action: He's been going to the gym every day this week. He's been going to the gym on Tuesdays and Thursdays lately. He loves going to the gym. Working out is his favorite thing to do.

There is really none. They are both informal ways of saying the same thing. There is a tiny difference in feeling. In its most literal sense, "heading" has the meaning of "going," but adds the meaning of an intended direction. "Where are you now?" "I'm heading north on I-95 to Boston." "Where are you now?" "I'm heading south on I-95 to Baltimore." Sometimes "heading" carries an idea of following a plan. "I'm heading for the gym, but I might stop at a coffee shop on the way."

If someone asked you "What are you doing today?", you could answer like this: "First I'm going to drop the kids off at school, then I'm going shopping, and then I'm going to the gym." It would sound strange if you answered like this: "First I'm heading to school to drop the kids off, then I'm heading to the grocery store to do the shopping, and then I'm heading to the gym." It would not be wrong, just very odd, because "heading" is a word with a precise meaning. It sounds odd to be heading many different places at the same time. "Going", on the other hand, has hundreds of meanings. It is very flexible.

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