Topping means cutting large limbs back to stubs, somewhere out in the middle of the branch, with no regard for where the tree can actually seal the wound. It is still the most common thing we see done to trees in Georgia yards, usually by somebody with a ladder, a pole saw, and a flat rate.
A tree seals cuts at the branch collar — the slight swelling where a limb meets the one that carries it. Cut there and the tree grows a ring of callus over the wound and closes it. Cut out in the middle of a limb and there is no collar to seal from. The stub dies back, decay walks down the inside of the branch, and the tree has no mechanism to stop it.
Then the regrowth makes it worse. A topped tree responds to losing its canopy by pushing dozens of fast, upright water sprouts from dormant buds just below the cuts. Those sprouts are attached to the outer bark layers only, not anchored into the wood — which means that five years later you have a dense crown of long, heavy limbs held on by the structural equivalent of tape, sitting directly above the decay the stub cuts started.
That is why the trees we are called to remove as hazards are so often trees that were topped. The homeowner paid once to make the tree dangerous and is now paying again, much more, to have it taken out.
Proper pruning does the same job without the bill at the end. Crown cleaning takes out the deadwood. Crown raising lifts the canopy off the roof and the driveway. End-weight reduction shortens heavy lateral limbs back to a side branch big enough to take over as the new leader — which lowers the leverage on the limb without leaving a stub. You get the clearance you wanted, and the tree keeps its shape and its structure.
If somebody quotes you a cheap price to "cut it back," ask where the cuts are going. The answer tells you everything about what you are buying.