【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.