let's consider this picture taken from Wikipedia,
It is written that:
A magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the size of the source is reduced to zero while keeping the magnetic moment constant. It is a magnetic analogue of the electric dipole, but the analogy is not perfect. In particular, a true magnetic monopole, the magnetic analogue of an electric charge, has never been observed in nature.
Because magnetic monopoles do not exist, the magnetic field at a large distance from any static magnetic source looks like the field of a dipole with the same dipole moment.
Now I have some basic doubts about the sentences in bold:
It is not clear to me how can the magnetic moment be the same as the size of the source becomes zero (which would mean the couple of poles becomes like a permanent magnet, where the North and South poles are inseparable, as shown in the highest picture on the left). As written there, the magnetic moment of a magnet can be defined as the product of the magnetic pole strength p and the distance l between the poles. To keep the magnetic moment constant and finite the the pole strength must be infinite. What does it mean physically?
What does it mean that the magnetic field generated from any of the four previous sources looks like the same at high distance? I understand that the fieldlines, apart from the inner region of the source, looks like the same. But, is it just a similarity of fieldlines, or, given one of those sources, is it possible to generate the same magnetic vector field in space (outside the inner region of the source) with one of the other sources if properly sized? Briefly: is it possible to generate the magnetic field vector of a magnet with a current loop in a 100% exact way?