Milky Way galaxy; the Galaxy
Specifically refers to our own galaxy, the Milky Way. In astronomy, it is the proper name for the galaxy that contains our solar system.
There are hundreds of billions of stars in the Milky Way galaxy.
A supermassive black hole is thought to exist at the center of the Milky Way.
galactic system; galaxy
A broader astronomical term for any galaxy or galactic system. Less common than 銀河 (ぎんが) for general 'galaxy'.
The Andromeda Galaxy is one of the nearest large galaxies to our Milky Way.