Since I've seen that galaxies are often called "deep sky objects", as opposed to individual stars, does this mean that all visible stars in the night sky actually only belong to The Milky Way Galaxy?
Or are there stars which belong at least to the galaxies in the Local Group?
I always thought that Milky Way was that lighter band (since it is said that the Galaxy is a "disc"), and that other stars might be part of other galaxies.
Yes all the stars you can see belong to the Milky Way galaxy. The Sun is located about two-thirds of the way out from the galactic center. Thus the band across the sky known as the "Milky Way" (from whence the galaxy name came) is the main disk of the galaxy. However, all the individual stars we see are still inside that disk, we just happen to be closer to them so that they stand out as individuals.
The galactic disk has a thickness to it (about 1000-2000 light years) so the closer stars are not all in the band we see as the main disk simply because they are closer and the relative angles between the sun and these stars puts them "up" higher than the main galactic disk as seen from Earth.
does this mean that all visible stars in the night sky actually only belong to The Milky Way Galaxy?
Yes. The only naked eye objects not part of the Milky Way Galaxy are the three or four galaxies visible to the naked eye: the two Magellanic Clouds, the Andromeda Galaxy, and possibly the Triangulum Galaxy.
Or are there stars which belong at least to the galaxies in the Local Group?
No, all the stars in other galaxies are too faint to be visible with the naked eye, with the brief exception of the supernova in the Large Magellanic Cloud, visible in 1987.
I always thought that Milky Way was that lighter band (since it is said that the Galaxy is a "disc"), and that other stars might be part of other galaxies.
The term "Milky Way" refers to two different things. Traditionally it referred to the pale milky band around the night sky, the result of the combined glow of millions of stars too faint to be seen with the naked eye. In the last century or so it has also been used to refer to our local Galaxy, which includes both this band and also all the stars in the sky, which are all in our particular region of the Milky Way Galaxy.
All stars visible to the naked eye belong to the Milky Way. The Milky Way is a very large, thin disk, and we lie in the middle of the disk, depthwise, and mostly to one side. This explains the band of the Milky Way being visible as a ring all the way around our sky and being maximally concentrated in one direction, towards the heart of the galaxy. However, thin is not infinitely thin, so there is still enough thickness in the disk that some Milky Way stars are visible above and below us.
