Gauss's law for magnetism can be written in two forms, a differential form and an integral form. These forms are equivalent due to the divergence theorem.
The name "Gauss's law for magnetism"[1] is not universally used. The law is also called "Absence of free magnetic poles".[2] (or some variant); one reference even explicitly says the law has "no name".[3] It is also referred to as the "transversality requirement"[4] because for plane waves it requires that the polarization be transverse to the direction of propagation.