The two frames have different axes.In the galactic frame, the Z axis is perpendicular to the galactic equator.ICRS and its predecessor FK5 are equatorial, with Z axis perpendicular to Earth's equator as of 2000-01-01.The angle between the different Z axes is ~63°.The transformation from one frame to the other is a 3D rotation.
Here is a Stellarium screenshot showing the J2000 equatorial grid in blue and the galactic coordinate grid in brown.