The M-H curves define the hysteresis behavior, the M-T curves define the thermal magnetizations which show the type of phase transition present by the magnetic system ( first- or second transition).
The "M" values in M-H (Magnetization vs. Magnetic Field) and M-T (Magnetization vs. Temperature) curves typically represent different physical properties and are measured under different conditions, so they can indeed be different.
In an M-H curve, the M value represents the magnetization of a material as a function of the applied magnetic field. This curve helps characterize the magnetic properties of a material, such as its saturation magnetization and coercivity.
In an M-T curve, the M value represents the magnetization of a material as a function of temperature, often measured under constant magnetic field conditions. This curve provides information about how the magnetization of a material changes with temperature, including phase transitions like ferromagnetic-paramagnetic transitions.
Since these curves measure different properties under different conditions, it's entirely possible for the M values to be different between the two curves. For example, a material might exhibit strong magnetic properties at low temperatures but lose its magnetization as temperature increases, resulting in different M values in M-H and M-T curves.