Magnetars are a subtype of one kind, which rotates rapidly and emits a pulse of electromagnetic radiation; that subtype is the pulsar.
AXPs and SGRs are probably a type of these objects with a strong magnetic field. Crust adjustments lead to starquakes in these objects, which increase in rotational speed during spin-ups and glitches. With a mass bounded by the Tolman-Oppenheimer-Volkoff limit, these stars are usually remnants of a core-collapse supernova. Magnetars are a subtype of one kind, which rotates rapidly and emits a pulse of electromagnetic radiation; that subtype is the pulsar. Held together by the degeneracy pressure of a certain subatomic particle, for 10 points, name this type of star composed of its namesake uncharged nucleon.
AXPs and SGRs are probably a type of these objects with a strong magnetic field.
{neutron} stars [prompt on {magnetar} or {pulsar} before mentioned]