Parody and Spoof

I observed Sarah uses 'parody' more, and I use 'spoof' more.  What is the difference between the two?  Sarah reckons there is a small difference between them.  Sarah reckon 'spoof' means a full-monty parody job, whereas parody can be a short mockery.  The dictionary seems to them they are synonymous.  I will probably still use 'spoof' and Sarah will still use 'parody'.