hi
in the two swing plane the hands tend to swing higher and the plane of the club is as you say between the toes and the ball, but in the one swing plane the swing is flater and arm is in line of the shoulders so its more out to past the ball a bit.
both types of swing work as does some mixing of the two but not all.
again the diffrent clubs also make a diffrence, a wedge makes you swing more upright and a driver more flat.
bill