Common phrases are draw drapes or shades, draw a bath (pull water?), draw a conclusion (out of someone) and other uses of pull. Why does draw mean pull? It becomes confusing when something that had a visualizable meaning - pulling drapes across a window - has been extended to something that does not make sense - turning Venetian blinds from the open position to closed position. How did this happen?
Oh Gosh, apparently "pull" is the original meaning of "draw", not producing artwork! Draw comes from a word meaning "to drag", so "drawing" a picture is about dragging the pencil across the paper! I guess I thought that producing artwork as a verb was important enough to have a word of its own, but apparently dragging things is more important. I hate language.
There is a children's book called 'Amelia Bedelia,' wherein a young girl is hired as a maid and takes things literally. When she is told to dress the chicken, she puts clothes on it, when she is told to dust the furniture, she throws powder on it, draw the drapes, she draws a picture, put out the lights, she hangs them all on the clothesline, and so on. Charming! But yes, in definition, as a verb, to move things towards each other, so water to a tub, curtains towards each other. I suspect the origin is European, but can't find that to be factual. Sounds British and formal, yes? Interesting question though, and thought provoking as to where some of these expressions really come from, love it, keep those brain cells circulating, language can be fun. Would be interesting if you asked a few children what they thought, like Amelia.