Answer
T2 and T2* are both dephasing; the difference is in the actions of each experiment to the qubit and what the expected results would be. For T2* and T2, you start by applying a Hadamard gate, which puts the qubit in a superposition state. Then, to calculate T2*, you wait a fixed amount of time and then apply a Hadamard gate again and take a measurement. Your results should have you back in the original state. However, if there is some dephasing, the results will then be in the opposite state. This is commonly referred to as a Ramsey experiment.
For T2, you wait half the fixed amount of time, and then apply a NOT (X) gate, and then wait the remaining (last half) of the fixed amount of time, and then apply a measurement. This is commonly referred to as the Hahn echo experiment.