In searching in vain for some photos of coppiced trees, I encountered the word "pollard".
It is a severe pruning of tree, but means only cutting branches near tips high in tree.
In the area where I live now, there are many trees that cannot expand their root
system enough to properly serve a tree over thirty feet high. Untended the trees
become susceptible to disease. So the tree surgeons cut off all of the limbs that
are over three or four inches in diameter. When I first saw one, I thought the
tree would die, but a year later there is a very healthy compact tree, again
able to give ample shade and reasonably attractive in appearance.
The word pollard in dictionary has first meaning a deer that has lost its horns.
What is done to the tree is comparable. The branches that are removed bear
similar proportion to horns on a deer.

So, would you think polling a tree just involves the branches and coppicing a tree involves the lower trunk?

The important thing is that neither kills the tree. Coppicing may involve just cutting of
some of the limbs, or with some species may be done close to ground. But pollarding
near where I now live, typically leaves no leaves or small branches, and top third of
tree is removed. I am astounded at how readily the trees again become attractive
and provide shade. The problem here is that lots are small, and trees cannot keep
enlarging their root systems. One of the first things I learned in botany (and one of
the few I remember) is that there has to be a balance between shoot and root.That's
why when one buys small trees, a good bit of the top has been removed, because
a lot of the tiny roots had to be sacrificed.