Why do people answer "I'm heading for__" to "where are you headed?"

[Eureka]

Hi, teachers!

I've got two questions about how to ask people where they are going.

First, when I'm on my way to the library and I met my friend, he's wondering where I'm going then can he say like this?:

My firend: Where are you going?
Where are you headed?
Where are you off to?

I think these expressions can be used interchangeably. I can't tell the difference among them.

If different, could you please tell me certain situation in which each expression can be used naturally?

My second question is why native speakers say "Where are you headed?"
not "Where are you heading?"

Suprisingly, they answer "I'm heading for the library" not "I'm headed for the brary" even if the other asks "where are you headed?"

If you help me understand, I really appreciate it. Have a nice day.

Thanks a million!

[Soup]

These can be used interchangeably,

Where are you headed?
Where are you off to?
Where are you going?

The difference between past simple headed and present continuous heading is very slight. It's one of motion, but the two are interchangeable. For example, Max sees Sam walking by and asks, "Where are you heading?" because Sam is on the move, moving towards a destination. Max could also ask, "Where are you headed?". No difference in the meaning expressed.

[BobK]

And the second question: if you think about it, 'headed' is a past participle. It isn't often used of someone who is in charge of their own movements:

He left London, heading for York.
He boarded a ship headed for Calais.

But, as Soup said, they are [I'd prefer an "often" or "nearly always" here] interchangeable.

b

[David L.]

Whilst some people may use them interchangeably, or more likely, invariably say 'headed for', I don't think that should deter from understanding the difference in meaning:

To ask, 'where are you headed?' is simply enquiring after the destination.

That the speaker uses the Present Continuous, 'where are you heading' denotes the speaker's perspective is of having caught the person en-route, 'mid-journey' to the destination. As such, the speaker's perspective is as much about the travelling towards, as it is the actual destination.
So - two people walking on campus bump into each other. One says, "Where are you heading?"
When told, say, "The library.", the speaker may respond, "I'm off to the chem. lab. for a practical. I'll come as far as the Physics building - give us a chance to arrange about Saturday."
Here, the perspective is of the possibility of journeying together in relation to their destinations.

A policeman might guess that a bankrobber is headed for the Mexican border after a job.
A radio dispatcher might say, "He was last seen heading for San Diego" since the perspective is the progress of the chase to catch him en route.