You would only get a different fruit if you had planted the seed from either the cherry or the plum and grown a new tree. Is this what you mean? Otherwise the fruit on the existing trees will remain identical as they are genetically identical to the tree.
What might have happened to your plum is that you have growth from below the graft and you are getting fruit from the rootstock, which might be a different kind of tree entirely, often a wild cherry plum type.

And since Plums are Prunus domestica and Cherries are Prunus avium, the chances of them crossing are extremely small to the point of vanishing.

Quite Owdb.