Since a circular magnet is specifically referred to, only "two annular end faces of an annular ring (one N-S)" may be realized in other cases but can not be called a circular magnet.
Toroidal magnets made of hard magnetic materials are not magnetically magnetized prior to magnetization.
Its pole position, pole pairs, depending on the way magnetization.
In fact, we can see a wide variety of ring magnets.
Some ring in the outer ring, there are one or more pairs of poles;
Some in the inner ring, there are one or more pairs of poles;
Some rings in the upper and lower two annular end (a N a S)
Some poles are in a ring-shaped end, with one or more pairs of poles