Accusing someone on the street could be classified as ordinary.
Accusing the president of the United States of blackmailing you is extraordinary.
Extraordinary: very unusual or remarkable. beyond what is usual, ordinary, regular, or established.
If I make the extraordinary claim that little green men exist on Mars, I’d best have quite a bit of proof to back it up.
OK first off, the person who invented that phrase (Carl Sagan) specifically decried the manner in which you are using it, and made that the basis for disowning his own quote.
Second, the logical and reasonable level of proof required in both the enumerated cases should be exactly the same. If it is not, the thinking is simply not based in logic.
A claim that may appear ordinary on its face may turn out to be quote extraordinary upon inspection, and vice versa.
Otherwise a single claim could be both true and false at the same time, depending ONLY on whether it was considered ordinary at the time the claim was made.