Could you explain the difference between 'to draw' and 'to pull'?

Question

Could you explain the difference between to draw and to pull to remember forever? I read about their difference, but I can not remember firmly. They appear in the text of the book often and alternately. I have even found a short sentence with both of them. Do they use that there was no tautology or they bring different meanings?

She found herself looking directly into one of his eyes, a great, amber cat's eye, the dark mandala of the pupil, opening, compelling, beckoning. She was drawn towards the oval, was pulled into it, was through it.

A Wind in the Door by Madeleine L'Engle

Answer 1

to be drawn towards something = to be attracted (physically or mentally) to an object or idea

• She has always been drawn to those books.
• He was always drawn towards math problems.

to be pulled toward something = to be physically moved towards something

• She was pulled into the current and swept out to sea.
• We were pulled by ropes up the mountain.

Answer 2

I've not read the original text but, unless the "oval" is some sort of physical (or metaphysical) device that could physically move her through it, both terms are expressing and emphasising her compulsion to approach and go through the "oval".

The difference is that, while "she was drawn" describes her compulsion directly (she is drawn; she is compelled); "she was pulled" is a metaphor for the same feeling, with the inferrence that she had no choice but to go through.

If the "oval" were a (meta)physical object, e.g. a portal, the text may be describing a physical force exerted by the oval, but it is more likely just a literary flourish, intended to make you feel the absense of choice that she felt.