Have been looking at this family and I don't think you will gain anything at all from the original marriage details as I'm sure you'll find her surname was indeed Jones.
According to census Mary Terry was bc.1786 Black Bourton, Oxfordshire.
Mary Jones bp.25/6/1786 Blackbourton, Oxfordshire, dau. of Jane Jones
Then we have:
Thomas Horn bp.28/6/1789 Blackbourton, son of William Horn and Jane.
Both these baptisms on familysearch.
Thomas Horn seems to be the only child baptised to William and Jane.
Sounds like Mary Jones - although born illegitimately - knew her father was William Horn and that sometime between her birth and 1789 (when Thomas Horn born) her mother Jane Jones married said William Horn and had son Thomas.
If all this is correct (although can't find a marriage between a William Horn and Jane (Jones or otherwise) then when Mary married she would have had to marry with her legal name of Jones, which in fact she did.
Therefore, the marriage entry is indeed correct - she was born Mary Jones and - regardless of whether she knew her father was William Horn - 'Jones' would be the name she would have to use when she married.
Unless a marriage can be found between a William Horn and Jane Jones I don't know how you can prove that Jane Jones and William Horn's wife Jane are one and the same but it sounds as if she was.
So, nothing wrong with the marriage entry - all accurate there - what's needed is a marriage between William Horn and Jane surely?
Annette