Headers

So I have heard that port and polishing your headers will give the same advantage as buy an aftermarket header.   I was just wondering the truth to this situation.  
Is it cheaper, expensive and what's the difference?  

You are talking about two different things. Whatever you do, what you want is maximum flow. You can get that in two ways - minimizing restriction and turbulence.

Polishing your factory headers will take away turbulence and improve flow. You will see some gain from doing this. However, you will still be stuck with your factory restriction.

If you buy aftermarket headers from a reputable source it is highly likely that you will see larger gains from your purchase than simply polishing your stock system.

This holds true for both intake and exhaust, but which one are you referring to?
What car is this for?

This all depends on the car you are dealing with, but factory intake and exhaust systems are usually poorly designed in terms of flow. They are also usually very restrictive but they are made to maximize reliability and minimize costs. A stock system will usually be optimized for a specific rpm range, usually between 2000 to 3500 rpm, since this is the range where the car will be driven most of the time.

Let's talk about length and width for a second. You may have noticed that the people here spend some time referring to lengths and diameters of independent throttle bodies, intake headers, exhausts, etc. Your exhaust and intake travels in pulses with each intake and exhaust stroke, creating a high pressure area for an intake (low pressure area for an exhaust) for a split second before the next time the intake or exhaust is opened up. (Do some reading on this, and you will know what I am talking about)When you design an exhaust system, you want to think about what your are trying to achieve - low end torque? High end power? or some good mid range pull? Think about the dragsters at the drag stip ... those long pipes sticking out from under their hood aren't there to just look cool and spit fire. They are carefully designed to provide optimal performance. Each one of those is for one cylinder and is probably wider than the exahust pipe on your car for all of your cylinders. BUT bigger is not always better. Their engines are running at around redline the entire time, thus the point at which their power needs to be optimized is at a much higher rpm with much higher number of exhaust pulses and volume

Depending on what you want, you will need to consider the diameter and length of your headers. If you want to get better fuel economy, go for a skinnier, longer exhaust. If high end power is your fancy, and you like to keep your revs higher, go for a wider, shorter exhaust. However, you have to remember that headers is just the beginning, you need to optimaze your entire exhaust system to free up the most power out of your engine. The same goes for the intake.

But in short, polishing will help you somewhat .. 1-4 hp to be optimistic, but aftermarket headers will really give you horses, up to 10-15 hp in some cases (and don't forget, you can polish those too!)

When it comes to polishing there is also a debate on how much you should polish and how much of a gain you will see. Some people support polishing, but they say that a perfect, mirror-shine finish will actually start to add turbulence. There are different schools of thought and the gains difference is too miniscule to measure.

I hope this helped, gimme your car model, so I can give you some more specific answers