Cassiopeia is a group of star forming fixed shape and position of stars do not change with respect to group members. So, it is regarded as constellation not galaxy.
Cassiopeia is five stars with distances varying between about 50 and 230 light years from Earth. They are not in any way gravitationally bound to each other, but are all, in cosmological terms, very near neighbors within our galaxy.Constellations are random groupings of a handful of very, very nearby stars. Galaxies are humongous clusters of stars which are scattered across almost all the universe we can see. A galaxy is a thousand times bigger and a billion times heavier than a constellation.