The boundaries of Weiss domains move easily in soft ferromagnets, so these return to zero magnetization. As opposed, the boundaries are pinned to impurities or dislocations in hard ferromagnets, which retain some magnetization.https://en.wikipedia.org/wiki/Ferromagnetismhttps://en.wikipedia.org/wiki/Magnetic_domain
All intermediate cases exist, with the hysteresis bigger or smaller, and how a material behaves depends much on impurities, previous deformations and heat history. But to my knowledge (not completely sure), the current temperature can suppress ferromagnetism altogether, not make the material reversibly soft or hard.
The words "soft" and "hard" ferromagnets come from steel, where most alloying elements and cold-working that harden it mechanically also increase the hysteresis. Though, there are exceptions even with steel, and usefully, other materials exist that combine the mechanical and magnetic properties differently.