What is the difference between "heading to" and "heading for"?

The difference between heading to and heading for is subtle enough that you can use them interchangeably, yet I think there is a difference.

If you are heading to somewhere, you have a strong expectation of getting there promptly.

If you are heading for somewhere, you are going in that route, but there is some possibility of not reaching it, or making of stops along the way. An even less definite phrase is heading towards.

For example, imagine I was having a night on the town and a friend phoned to find out where I am. If I said:

"I'm at the bottom of town now, but I am heading to the top of town."

... then my friend would probably infer that he should meet me in a pub at the top of town. If I instead said:

"I'm at the bottom of town now, but I am heading for the top of town."

... then my friend is more likely to infer that he should meet me in some pub along that route.

There is an equally subtle difference between heading and headed. Once more, you can use them interchangeably, but heading is more active, and headed is more passive.

If you are the driver of a vehicle, or walking or running, you would be more likely to say heading.

If you are a passenger in a vehicle, or you're walking or running but you're following a leader rather than navigating yourself, you would be more likely to say headed.

Native speakers are unlikely to say either. What you might hear is I’m heading for the airport now.

Heading to somewhere is deliberate. It denotes an intended destination.

The plane is heading to Dubai.

Heading for somewhere is not always deliberate, and denotes a direction rather than a destination.

Oh, no! The plane is heading for those mountains!

You can also use "for" with the intended destination...

The plane is heading for Dubai.

...however, you can't always tell whether that really is the destination if you do that.

The plane is heading for Dubai at the moment, and will turn towards Cairo once it clears the English Channel.

Lots of people have given similar answers. Hopefully these examples illustrate the point in a way which clarifies any confusion.