Meaning : Not easy to believe.
Example :
Incredibly, she survived the crash.
Synonyms : implausibly, improbably, unbelievably
Easy to believe on the basis of available evidence.
He talked plausibly before the committee.Meaning : Exceedingly. Extremely.
Example :
She plays fabulously well.
Behind you the coastal hills plunge to the incredibly blue sea backed by the Turkish mountains.
Synonyms : fabulously, fantastically