Plant identification

catherine.hicks1

Could someone please explain how two trees with different leaves appear to be growing from the same rootstock

MuddyFork

I would suggest that this is a grafted tree and the green branches are growing from below the graft and are the original plant.  Normally you would ensure that the graft is below the soil to stop this happening.

Dovefromabove

I think you’ll find that the finer leaved variety has been grafted onto another type of average rootstock. Now the stronger growing rootstock has sent up some shoots from below the graft and they will outgrow the more decorative variety which has been grafted onto it. 
Remove the shoots growing from the rootstock with sharp secateurs and keep an eye open for new shoots from below the graft and remove them as soon as they appear.