It would have been the head of the household who gave the information to the enumerator and that could often mean their best guess sometimes, age was not as precise a necessity and i they didn'r have the familt bible to hand to check the dates of birth then they might well get it wrong. If she was 20 when she married she would have needed her father's permission as she would be under age.
Banns books sometimes help , they would be with the Parish Records, in Scotland they could marry anyewhere though not necessarily a church.
They married before civil registration started in Scotland and so you need to either locate the banns.
Why two quite different fathers names are given is another problem, but bearing in mind her son registered the death, it must have been the information he had, could Jane's mother have remarried? Also, have you looked at any of her siblings marriages to see what they recorded as their parents?