804 is a reissue of a long-standing exemption to allow joint owners of aircraft with a private C of A to do tests and paid refresher training in their own aircraft. It doesn't have much relevance these days, though I suppose it does technically permit the pilot undergoing the training to be pilot-in-command, which might be useful in some circumstances.
Only 802 and 803 are relevant to permit aircraft:
802 permits paid training for any purpose (other than instruction for a licence or rating) where the pilot already holds an appropriate licence and rating
803 permits paid training and testing for the purpose of revalidation etc. where the pilot doesn't hold a current rating