The muon g-2 test is 40,000 times more sensitive to the Standard Model extensions compared to the electron. The muon, electron, and tau are generically referred to as charged leptons, and they have the remarkable property that they are believed to be point particles. Contrast this with, say, a proton, which is made up of quarks. The electron is a stable particle, while the muon and tau are radioactive and decay after some period of time. All muons spin on their axes like a toy top or the earth on its polar axis.
All muons spin at the same rate.
When we speak of spin direction we mean the direction of the axis of rotation. In the muon g-2 experiment, when the muons are first injected into the storage ring, they are polarized along their direction of motion. The north and south poles of the muon magnet are aligned along the direction of the spin. The strength of the magnet is indicated by the magnitude of the magnetic moment. Its value is sensitive to detailed properties of the muon, and its measurement is an excellent test of models which predict these properties.