Galaxy Morphology can be studied at several places including galaxyzoo.org and Wikipedia. The basic chart defining galaxy morphology started with Hubble.
The Tuning Fork of the Hubble Sequence. From this model we get the basics. He was missing a few types, but overall he showed the relation of one type to another on a chart. Fantastic for 1936. This is still the main concept used in Modern Astronomy. There is a more modern version of galaxy taxonomy which includes a mapping of individual stars within the galaxy. The MK or Morgan Keenan system evaluates spectra. It is vital that we understand these systems and expand upon them as needed.
To understand the differences between galaxies we need to understand their Galactic Core. Galactic Cores are not Black Holes. They are incredible densities of Baryonic matter that EMIT magnetism and densities. Here we see a Galactic Core emit a star like a CME (Coronal Mass Ejection) or a Solar Flare.
The above shows the plane of the Milky Way Galaxy. It has a Northern Ridge and a Southern Ridge coming from a core. This means its a highly dense Baryonic matter object rotating at high speed and is so hot that it emits stars in great quantity. It is also obvious that the Magnetosphere of the Milky Way Galaxy is on the left of this chart and the bending towards the right. This shows leftward motion of the galaxy in the Galactic Supercluster. The right side of this chart shows a magnetic event that is similar to the petite tail of the Earth's Magnetosphere.
This article The Corrugated Galaxy shows the plane of the galaxy is not flat but corrugated. This comes from the nature of the magnetic Galactic Core. We know the flare that occur on the sun occur when a magnetic line snaps, dragging material with the snap. The sun cycles solar activity. The most intense activity occurs on the equatorial region. This is the chart for the Sunspots over the last 400 years.
Spiral Galaxies being a very large stars ejects material in its active phases just like the sun. When I look a the pic for the Milky Way Galaxy, I count 7 to 8 arms. There are probably billions of stars in each arm of the galaxy. This material ejected over time reaches the area where the magnetic influence of the core rotation reduces. Then we see the reduction of speed of all the stars in the arm. There is also the interaction of Dark Matter against the arms. When every period of activity ends for the galaxy, Dark Matter rapidly fills in between the arms.