Genetics research is the cutting edge, these days. So, it's all very modern to define evolution as "a change in allele frequencies in a gene pool".
Not everyone likes this definition. For one thing, it is incredibly expensive to measure genetic material. And, in fact, the majority of mutations have no visible effect. So, if two beetles look and act the same, is anyone really going to spend millions to search for subtle differences?
For most situations, it's much more practical to define evolution as a change in the observable characteristics of a population. Ah, but what's a population? It's hard enough to define a species. And to an ecologist, a population is a biome - a region containing a whole community of species.
And, what's an observable change? When all you have is fossilized bone, you wind up defining evolution as a change in bone structure - as a morphological change.
So, the bottom line is that we're stuck with using several slightly different definitions. What they have in common is that they deal with biology, with inherited characteristics, and with measurable change over time. And, they are never about individuals.