In my field study Environment Eng. disaster is used for natural happenings which cause irreparable results in the nature and human beings' lives, but I have seen and read people use them for different or similar matters. Could you please make clear what the correct usage of those terms is?
This website describes the difference between a disaster and a catastrophe as follows:
Natural disasters occur when extreme magnitude events of stochastic natural processes cause severe damage to society. "Catastrophe" is used about an extreme disaster, although originally both referred only to extreme events (disaster is from Latin, catastrope from Greek).
In my own understanding of the words, I would describe a catastrophe to be a disaster of such high magnitude that you could not have prepared for it, because you would not have expected that something so bad could happen.
EDIT: @J.R. reminded me about the less literal usage of the two words, which you could use to say that things turned out badly, for example:
How was your performance last night?
Oh, it was a disaster – the percussion was off, the woodwinds squeaked, and the soloist couldn't hit her high notes.
In this hyperbolic form, I believe that disaster is more common, but you could use catastrophe if you really want to exaggerate.
When Disraeli, then out of power, was asked the exact same question, he explained:
"If Mr. Gladstone [Disraeli's rival and then Prime minister] fell into the Thames, it would be a disaster.
But if some over-zealous person jumped and pulled him out, it would be a catastrophe."
(Here is a reference)