I've seen the terms mutual and magnetizing inductance used interchangeably, but I don't believe them to be the same. Mutual inductance can be derived if you consider a simple magnetic circuit with two separately excited coils (such as the one shown here: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/transf.html). The flux linkage in coil 2 that is produced by the current flowing in coil 1 is related to mutual inductance (lamda21 = L21*i1, where "L21" is the mutual inductance term). You can derive the same relationship for the flux linking coil 1 due to the current in coil 2 (lamda12 = L12*i2). In theory, L12 = L21 = the mutual inductance.
Magnetizing inductance is associated with the flux that actually links the core of the transformer (as opposed to leakage flux, which does not). If you're familiar with the 'open circuit test' for a transformer that's used to measure Xm, think about how the test is performed. The secondary is left open while rated voltage is applied to the primary. This test actually measures primary side leakage and magnetizing reactance, but the former is typically assumed to be much smaller, and is therefore neglected. This is more closely related to the self-inductance of one side (in this case the primary) of the transformer.
The Magnetizing inductance / reactance can be referred to either the primary or the secondary of the transformer. For example, if you use the open circuit test as described above, you would include it in the primary of your model. You can then use the turns ratio to refer it to the secondary.