The major geocentric coordinate systems used in the Space physics:

The Equatorial Inertial (GEI) coordinate system:

• The X GEI axis is directed to the point of the spring equinox,
• The Z GEI axis is coincide with the Earth's rotation axis,
• The Y GEI supplements the right three.

The Geographic (GEO) coordinate system:

• The Z GEO axis is coincide with the Earth's rotation axis,
• The X GEO axis belong to the Greenwich meridian,
• The Y GEO supplements the right three.

The Solar-Ecliptic (SE) or (GSE) coordinate system:

• The X SE axis is coincide with the direction to the Sun,
• The Z SE axis is directed to the Ecliptic Pole,
• The Y SE supplements the right three, toward to the dusk.

The Solar Magnetospheric (GSM) coordinate system:

• The X GSM axis is coincide with the direction to the Sun,
• The XZ GSM plane contains the dipole axis,
• The Y GSM supplements the right three, toward to the dusk.

The Solar Magnetic (SM) coordinate system:

• The Z SM axis is coincide with the geomagnetic dipole axis,
• The XZ SM plane contains the Earth-Sun direction,
• The Y SM supplements the right three, toward to the dusk.

The Magnetic (MAG) coordinate system:

• The Z MAG axis is coincide with the geomagnetic dipole axis,
• The X MAG axis belongs to the geographical meridian, which contain the magnetic dipole pole.
• The Y GSM supplements the right three, belong to the intersection of the geographical and geomagnetic equatorial planes.

About space physics coordinate transformation see Russel [1971] and Hapgood [1992]

Reference

1. Russell C.T. Geophysical coordinate transformation // Cosmic .Electrodyn. 1971. V. 2. P. 184-196.
2. M.A. Hapgood, Space physics coordinate transformations: A user guide // Planet Space Sci. 1992. V. 40, P. 711-717