The new stone looked like Jon's stone but wasn't. It was the true reality stone. Though changes made by it were treated as normal it did not change reality to explain it or to fit the new wish.
For example if Jon was mad at Zoe and used his old stone to wish Zoe to be a cow, she would become a normal acting cow in a field, and jon would likely live on a farm or ranch and own other cows, some of which may be karens new parents.
But the true reality stone would turn karen into a cow also but she would keep her old goth personality, her make up, her clothes, and still be regarded as jons sister. Jons mom would have given birth to her. But reality would NOT go out of its way to explain why jons sister is a cow, people would just accept it. It also would not make a similar effect done by another magic (curse from a wish, etc.) seem normal, just the one from this stone.
Another example of the differences would be what happens if Jon wished Sarah Macmillain and Leonard Drullers would swap bodies and they did not hear it.
With his old stone sarah (in leonards body) would get a male version of her personality and be a preppy guy (likely into a preppy sport like track, tennis, or soccer) and have a thin, handsome version of leonards body that it would develope intio with sarahs personality. Meanwhile leonard (in sarah) would have a fat version of sarahs body and a female nerds personality.
With the true reality stone Sarah in leonards body would still have sarahs feminine personality and clothes but in leonards fat hairy body, and leonard would have a male geeky personality and clothes in sarahs thin sexy body. They would see it as normal (unless they heard it) and so would everyone else, but reality would not change to explain it, or change to make their minds and bodies change to fit a new reality.