Adapted from an amazing book entitled Introduction to Functional Magnetic Resonance Imaging: Principles and Techniques (2nd Ed) by Richard B. Buxton (one of my MRI professors at UCSD!):

T2

1. The individual dipoles that sum up to produce the transverse magnetization are not precessing at precisely the same rate
2. As a water molecule tumbles due to thermal motions, each H nucleus feels a small, randomly varying magnetic field in addition to B0 due primarily to the other H nucleus in the molecule.
3. When the random field adds to B0, the dipole precesses a little faster, and when it subtracts from B0, it precesses a little slower.
4. For each nucleus the pattern of random fields is different, so as time goes on the dipoles get progressively more out of phase with one another, and as a result no longer add coherently.
5. The net precessing magnetization then decays away exponentially, and the time constant for this decay to 63% of its original value is called T2.

T2*

1. The source of this T2* effect is magnetic field inhomogeneity.
2. Because the precession frequency of the local transverse magnetization is proportional to the local magnetic field, any field inhomogeneity will lead to a range of precession rates.
3. Over time the precessing magnetization vectors will get out of phase with one another so that they no longer add coherently to form the net magnetization.
4. As a result, the net signal is reduced because of this destructive interference.
5. The T2* effect, is due to static field offsets rather than fluctuating fields (as in T2).

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In my words (hopefully this helps somebody):

While both T2 and T2* decay occur because of inconsistent magnetic fields causing differences in precession rates leading to spins growing out of phase and ending in destructive interference, the difference between T2 and T2* is that in T2 the source of the magnetic field inhomogeneity is the random motion of water molecules moving hydrogen nuclei near each other and in T2* the source is static magnetic field inhomogeneities within the MRI itself in addition to T2 effects. This is why T2* is always shorter than T2. Reasoning that T2 is a theoretical constant and that T2* is an observed measure is not alone sufficient for explaining this difference, however it should be noted that T2* is always faster than T2 decay. Some sources also say that T2 is measured over 5-10 microns and that T2* is measured in the millimeter range, but im not sure if thats useful.