In my limited knowledge:
Mushing is when you have a full team of dogs pulling some variety of traditional dog sled
Carting is when you have a single dog pulling a dog cart which typically will not be holding a person
Sulky driving is having one or two dogs pulling a specialized cart (a sulky) which can hold a single person (obviously you need dogs of a certain size and conditioning to do this one)
Joring is when you have one or more dog that helps pulling you as you also provide some of your own power: this can be just with running (also called canicross), but also with skiing, biking, kickbiking, scootering, etc. This is a good option for dogs who wouldn't otherwise be big enough to safely pull a person 100% by their own power.
I've never done any of these sports personally, so I may have some things mixed up, but that's my general understanding of the 'dog pulling things' sports that aren't weight pull. Any of these will require a dog to be trained and conditioned carefully so they have the appropriate muscle development before they're ever expected to pull the sled/cart/etc. and all require specialized harnesses to distribute the force in a safe and effective way (but it's not a one harness fits all situation, heavier pulling with a low attachment point might require a more specialized harness with a spreader bar whereas joring harnesses are typically more lightweight).
Mushing is when you have a full team of dogs pulling some variety of traditional dog sled
Carting is when you have a single dog pulling a dog cart which typically will not be holding a person
Sulky driving is having one or two dogs pulling a specialized cart (a sulky) which can hold a single person (obviously you need dogs of a certain size and conditioning to do this one)
Joring is when you have one or more dog that helps pulling you as you also provide some of your own power: this can be just with running (also called canicross), but also with skiing, biking, kickbiking, scootering, etc. This is a good option for dogs who wouldn't otherwise be big enough to safely pull a person 100% by their own power.
I've never done any of these sports personally, so I may have some things mixed up, but that's my general understanding of the 'dog pulling things' sports that aren't weight pull. Any of these will require a dog to be trained and conditioned carefully so they have the appropriate muscle development before they're ever expected to pull the sled/cart/etc. and all require specialized harnesses to distribute the force in a safe and effective way (but it's not a one harness fits all situation, heavier pulling with a low attachment point might require a more specialized harness with a spreader bar whereas joring harnesses are typically more lightweight).
