The phys.org link does have this relevant statement as to why those two are a different type of thing:
> Although other types of magnetism, such as diamagnetism and paramagnetism have been categorized, these describe specific responses to externally applied magnetic fields rather than spontaneous magnetic orderings in materials.
> Although other types of magnetism, such as diamagnetism and paramagnetism have been categorized, these describe specific responses to externally applied magnetic fields rather than spontaneous magnetic orderings in materials.