Often there is a spherical central bulge of stars. Our Milky Way galaxy is a spiral galaxy. The spiral arms are waves of star formation swirling around the galaxy. The new young stars are hot and bright, they light up the gas and dust in the arms. Some spirals have a bright bar across their central regions, these are called barred spirals.
Elliptical galaxies are vast ellipsoids of stars.
Some are spheres. Irregular galaxies are, well, irregular. Early galaxies that had not evolved to their mature shapes. Some photos show galaxies interacting with each other. We know that the Andromeda galaxy will collide with our Milky Way galaxy in a hundred million years or so.