Another item which might help an understanding of slip and skid is how the balance ball works.
It is influenced by gravity and centrifugal force. In a slip (as when starting a turn as mentioned above) it is gravity which causes the ball to be off centre towards the inside of the turn. In a skid, it is centrifugal force which takes it the other way.
I find it easy to imagine that anyone first learning about this could think that the ball should be on the opposite side i.e away from the direction that the aircraft is slipping or skidding.