M stands for magnetization, Ms for saturation magnetization. Most magnetometry experiments determine the component of the specimen magnetic moment vector along the magnetic field, which needs not be the modulus of magnetization (neither microscopically nor macroscopically). It all depends on the material in question and on how magnetization reversal occurs.
A specifically simple example is the case of homogeneous rotation of magnetization. In the presence of uniaxial anisotropy, this is commonly referred to as as the Stoner Wohlfahrt model of magnetization reversal.
It might be worthwhile for you to contemplate the different modes of magnetization reversal in a good textbook on magnetism.