I attached the requested diagram.
In the case of the magnetic field in a bar by convention, the direction of the field is taken out of the north pole and towards the south pole of the magnet. These types of images are commonly made of some ferrous material.
In the case of the horseshoe magnet, the highly concentrated magnetic field is distinguished between its legs. In the figure it is shown in a contribution from North to South, again by agreement, however outside the two poles, the magnetic field falls rapidly. A horseshoe magnet is basically a bent bar magnet.