* Drag is a verb that means to pull something along the ground or other surface, often with effort. It evolved from the Old English word "dragan", which itself is from the Proto-Germanic *draugan. This word is ultimately derived from the Proto-Indo-European root *dreg-, meaning "to pull".
* Draw can mean to pull something towards you, to create a picture, or to attract someone's attention. It comes directly from the Old English word "drāgan", which also means "to draw". This word is also descended from the same Proto-Indo-European root *dreg-, meaning "to pull".
So, even though "drag" and "draw" have slightly different meanings, they share the same root word and ultimately the same meaning: to pull something.