Pull, draw, drag, haul, hale, tug, tow mean to cause to move in the direction determined by the person or thing that exerts force.
Pull, the general term, is often accompanied by an adverb or adverbial phrase to indicate the direction.
Draw usually implies a pulling forward or toward the person or thing that exerts the force; commonly it implies a steadier and smoother and often gentler motion than pull .
In extended use draw often specifically implies a result dependent on a drawing by lot or by extracting or by an inferring or by attracting or a bringing forth or eliciting from a source of supply.
Drag implies a pulling slowly and heavily after the agent or thing exerting force over the ground or a surface; it usually suggests active or passive resistance.
Haul implies a forcible pulling, sometimes a dragging.
Haul may imply transportation of heavy materials in a vehicle or conveyance.
Hale may occasionally replace haul in the sense of pulling forcibly, but more often it is used of the constraining, compelling, or dragging of a reluctant person.
Tug implies a strenuous, usually spasmodic pulling, but it may or may not suggest actual movement.
Tow implies pulling or drawing (as by a rope or chain) something which is not using or is unable to use its own power.