No. Both words are synonyms.
True Hoax would be an oxymoron.
The term is an oxymoron, which pairs apparently contradictory terms to create a specific, often poetic meaning. Examples include deafening silence, hated affection, or mercy killing.
Re: the term for a contradiction of words, you are probably thinking of 'oxymoron.'
oxymoron
No. An oxymoron is a literary term for something that inherently contradicts itself, often in a humorous way, but the phrase would be made up of normal adjectives and nouns.
George Carlin referred to "military intelligence" as an oxymoron in one of his comedy performances.
It means fake.
fake, phony
Hoax
Yes original copy is an oxymoron
hoax
phony
The term 'jumbo shrimp' is an example of an oxymoron. The term 'military intelligence' is not a true oxymoron, but it seems that way sometimes. He was not the first veterinarian to discover that a 'small elephant' was an oxymoron.
Fake
it is a website hoax
It was a "fake dead reggae star" hoax
oxymoron (literary term)
The term, scientific religion, is an oxymoron. There is no such thing.