Most people I know use drafting and carting interchangeably. Drafting or
carting is usually pulling a cart, wagon, or travois. These apparatuses have
shafts and brakes so that the rig can be maneuvered through turns. IMO,
drafting or carting (whichever term one prefers to use) is not about sheer
weight, but rather about how well the dog and handler can maneuver a cart to do
everyday farm activities.

Weight pull is the activity that involves heavy duty pulling. During weight
pull competitions there are no shafts, and the goals is to test how much weight
a dog can pull. The weight can be either on a cart(wheels or rails) or on a
sled on snow. Weight pull carts and sleds do not have shafts as the goal is not
about maneuverability, but about weight pull only. For people who do use their
dogs on the farm to do work, I usually hear the terms hauling or pulling. I
only hear the specific term weight pull when speaking about the sport.

Just to make things confusing, it is common to cross train dogs in both sports
to improve both sports. My dogs are active in both drafting/carting and weight
pull. I might have my dog pull a 100 lb load in his draft cart to train for
weight pull for a miles to build endurance. Or I might have might dog
participate in weight pull to build up strength and confidence.

To make things even more confusing, if you look through breed club rules and
titles, most all carting/drafting titles are called Draft titles or Draft tests,
even though people refer to it as carting. ND stands for novice draft. DD
stands for draft dog (the open title in GSMD). There’s also team draft which is
sometimes referred to as brace.