Correct is kinda like concealer - in fact, they look pretty much the same.
They just have slightly different purposes.
A 'normal' concealer is designed to cover blemishes/colour which is why we say it gives us 'coverage'.
Whereas, the corrector product is not designed to give coverage. Instead, it's purpose is to take out the blue/purple colour under our eyes which is what we call 'correcting'.
Which kinda is like taking you to square 1 - getting under your eyes to the same (or close enough) colour as the rest of your face.
That's why correctors have the colour orange in them, because that's the cool science behind the colour wheel - orange onto blue cancels out the colour all together.
Anyway! That's as technical as I am going to get here, but, I hope that has given an easy explanation on what this orange product thing is and why you need it.
The reason you don't see it often is because it's not a staple item like a foundation, it's more of a 'next level' product for those, like you my friend, who have dark under eyes circles and need some extra help.
The final thing to note is that orange correctors also come in light-dark shades just like foundations. If you have pale skin, I recommend a really light peach, medium skin colour, an orange corrector and if you have dark skin, a rich red corrector.