You could imagine the curved parentheses as "cutting the corner" of the square brackets - or imagine the curve as just gently kissing the endpoint at a single p

You could imagine the curved parentheses as "cutting the corner" of the square brackets - or imagine the curve as just gently kissing the endpoint at a single point, while the flat square solidly includes it. "Open" makes sense because it satisfies the criterion that for any number in the interval, you can find a larger (or smaller) number that is also in it - there's "no end".