The Theory of Evolution is the theory that all the living forms in the world have arisen from a single source which itself arose naturally from an inorganic form.
This encapsulates what I see as the problem creationists have in trying to describe evolution (this is in a biological context), because creationists view evolution as an opposing theory to the genesis narrative which starts of “in the beginning…”. This results in creationists shunting in abiogenesis and ideas about common ancestry into the theory of evolution because they are coming into it from the opposite direction from Science.
By contrast scientists have to work with the evidence available to them, which both in Darwins time and today is predominately modern species and to some extent the expanding collection of fossilised specimens. So for example they can compare the fully sequenced genome of the tiger and domestic cat and find they are 95.6% similar, as well as calculate the mutation rate giving 10.8 MYA since the species diverged. But this same line of enquiry can be used to compare the human and gorilla genomes and gives a 94.8% similarity, with the populations diverging approximately 8.8 MYA link.
So with the evidence we have from the present we have been able to tunnel into the past to identify how modern species have converged into common ancestors. The existence of fossils providing snapshots of the species which existed at the times of these divergences have been a bonus, a chance to understand the processes involved. This line of evidence does lead to the potential of a LUCA, but it is a consequence of the evidence, not a prerequisite of the theory.
As to the topic I think RAZD’s first example in Message 3 is howI would go about describing evolution. Firstly it describes evolution over generations. There is the obvious distinction over how many generations a feature infers micro or macroevolutionary change. But this also leads into the more subtle idea of fitness. There is a tendency to look at fitness in terms of the individual or the population to define fitness. However, for an individual to be fit it must not just survive, it must contribute to the next generation. The more ‘fit’ an individual is can be determined by how long it is able to survives, how capable it is at mitigating selective pressures such as sourcing food, avoiding predators, recovering from disease; all of which affects the number of offspring it can contribute to the next generation.