Not much, the two terms are synonymous.
A spoof.
parody
hoax - parody
Spoof comedy and parody comedy are closely related genres but not exactly the same. Spoof comedy relies on exaggerating and satirizing specific elements of a film or genre, while parody comedy uses humor to imitate or mimic a specific work or style in a humorous way. Both spoof and parody comedy aim to entertain by poking fun at the conventions of a particular genre, but with slightly different approaches.
coda and twist
satire charade lampoon mockery put-on spoof
Squidbillies - 2005 Gimmicky Magazine Show Spoof Parody About Dan Halen 3-14 was released on: USA: 27 April 2008
A spoof is a specific type of parody that typically involves imitating or mocking another work, often in a humorous way.
One common synonym for parody is "farce." Others include "spoof" and "tie-in."
There has not bee a spoof of Nightmare On Elm Street as of yet.There is a parody of Scream and Friday The 13th called Shriek If You Know What I Did Last Friday The Thirteenth.
If it's really a "spoof", you may be protected by the laws that allow use of copyrighted materials for parody of the original.
One of the highly contested areas of fair use is parody. It is entirely possible to create a parody of something, without a license, within the law, but you'd be treading a fine line.