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A galaxy plane refers to the mid-plane of the flat portion of a disk galaxy, generally that with the highest density of stars. When referred to as the galactic plane (and otherwise unqualified), it generally means that of the Milky Way. It is often used in general descriptions of the position of astronomical object in the region of the Milky Way, e.g., describing the general position of a particular globular cluster.
The galactic plane is also used for a precisely-defined nominal determination of the Milky Way's galactic plane which is a basis for the current standard galactic coordinate system. IAU's standard galactic north, used by the coordinate system, is the direction perpendicular to this plane. The visible Milky Way is close to flat, but does have some thickness. The galactic equator is the great circle around the celestial sphere corresponding to this standardized galactic plane. The galactic poles are the directions into the sky perpendicular to this plane, roughly matching the directions of the axis through the center of the Milky Way (galactic center) around which the Milky Way disk rotates.