The equatorial mount is aligned to the axis of the Earth and follows the stars in a circular arc. You only need to control one axis instead of two in order to keep an object in the centre of the visual field. Convenient for observing and essential for astrophotography.
The two mounts look different, but the principle is the same: they consists of two slewing axes.
The right ascension axis is aligned to the celestial North Pole close to Polaris, so that it is parallel to the rotational axis of the Earth. A polar finder helps with the alignment. The declination axis is perpendicular at ninety degrees.