there are some differences between these words , which are :
Yank :
(informal) to pull someone/something hard, quickly and suddenly:
e.g : He yanked her to her feet
i yanked the door open.
Tug:
to pull sth hard, often several times:
e.g : She tugged at his sleeve to get his attention.
(figurative) a sad story that tugs at your heartstrings (= makes you feel sad)
Haul :
to pull sth/sb with a lot of effort:
e.g : The wagons were hauled by horses.
He reached down and hauled Liz up onto the wall.
Source : Oxford Advanced Learner's Dictionary