The evolution of a galaxy is nothing else than the evolution of its constituents, the stars, the gas and the dust. Also the central black hole. Each of them have its own evolution, in addition to the evolution of the ensemble. Here comes the notion of complexity: the evolution of a galaxy is more than its evolution as a whole or the added evolutions of each of its components.
Individual stars evolve according to their mass and metallicity. Their number in a galaxy is not constant when stars are formed, accreted, ejected. Also, their distribution and kinematics across the galaxy change when there is a gravitational perturbation, either internal (instability) or external (interaction with another galaxy or a dark matter halo).
For the gas, it is even more complicated since a cloud of gas can be compressed or diluted, its composition can be modified when a star explodes and injects enriched material. Radiation of stars also affects the temperature and pressure, possibly inducing chemical reactions. Gas is very sensitive to gravitation and winds, and it can condense to form new stars.
The dust behaves like gas, with more complex chemical processes, and condense into stars.
Galactic nuclei, most often with a massive black hole at the center, is probably fed through modifications of the orbits of stars and distribution of gas and dust. This can occur through internal or external perturbations.
Global structural properties of galaxies, like ellipsoids, disks, spiral arms, bars, bulges, are merely visible tracers of the distribution and kinematics of the constituents, mainly stars in visible light.
The evolution of a galaxy is thus the evolutions of all these components and their interactions. To describe the evolutionary state of a galaxy, we need observables that can trace the evolutionary states of the components.
The evolution of a galaxy is a continuous process. Evolution means modification with time. Galaxies on average have changed since the beginning of the Universe. This evolution is the evolution of a whole population. This is not the evolution of a galaxy. The former describes the modification of global properties averaged over quite different kinds of objects. The latter strongly depends on the constituents of a galaxy, and this cannot be identical for all galaxies. Thus the evolution of galaxies is obviously a diversified process.
In addition, “evolution” can be easily understood for a single entity, being a whole population, a single object or a single parameter. Being more or less evolved has a clear meaning. But when some complexity occur, it becomes rapidly awkward. For instance, is a massive metal-poor galaxy more or less evolved than a small metal-rich galaxy? On average over the whole galaxy population, metallicity and mass increase with time, because metals are produced within stars and gravity attracts more mass. These are two contradictory indicators, then it is impossible to tell which is the most evolved. One can say that they are equally evolved, having followed two different pathways. In other words, they diverged from a common ancestor which was small and metal-poor. Then, can we still compare the two distinct evolutions in term of more or less? This is exactly why biologists have proved that “diversification” is much more appropriate and can cope with very complex situations.
When a modification is invoked, a starting point or state is necessarily implied. This is what formation should mean, the formation of the object as it is before the modification. In other words, the formation of the galaxy as we observe it. Hence, “formation of galaxies” is generally confusing since it may be understood (and I think it is most often) as the formation of the first objects that could be called “galaxies” (by the way, what is a galaxy?). But they did not form all at the same time in the state we see them!
As a conclusion, the current astronomical challenge to understand the “formation and evolution of galaxies” is an ill-defined problem. It is simpler to mean “formation of galaxies” as the way they could have appeared for the first time in the Universe, “evolution of galaxies” as the change with time of some galaxy property averaged over the entire population of galaxies, and to use “diversification of galaxies” to encompass the modifications of individual galaxies through transforming processes that take a galaxy in a starting state and change it to another evolutionary state. Thus, the challenge of astronomers is to understand the general evolution of galaxies like biologists with the evolution of species, and study the diversity of galaxies like biodiversity, looking for the mechanisms of appearance and disappearances of the species.
Altogether, the current challenge is to understand the diversification of galaxies, which means how the observed diversity have been generated. Am I wrong?