Asked about the distinction between Paley's design argument and St. Thomas Aquinas' Fifth Way, he obligingly answered:
Teleology can be either inherent in the nature of a thing (as an acorn has an inherent tendency to become an oak) or imposed from outside (as the materials that make up a coffee machine have no inherent tendency at all to make coffee, but must be forced to do so by an artisan). The former, immanent sort of teleology is what Aristotelians mean by final cause, and what Aquinas is interested in in the Fifth Way. When one denies final causes, the only sort of teleology left is the latter, extrinsic sort, which is what Paley is interested in. Hence the design argument's tendency to characterize the world as a machine or artifact.
For Aquinas, by contrast, final causality is evident in nature precisely insofar as it is not like an artifact[bold mine -kjj]. This is also why complexity matters so much to design argument defenders but not to Aquinas: Artifact-like objects can seem impossible to account for in terms of impersonal processes only to the extent that they are so intricate that their resulting from such processes is improbable. For Aquinas, by contrast, even something extremely simple like a match's tendency always to generate heat and flame specifically, unless impeded from outside, is an unmistakable mark of final causality. And for this reason, finality exists wherever regular causal patterns do (which is of course everywhere in nature, down to the level of basic physics); complex biological phenomena are not particularly important for the argument, being just one, fairly uncommon instance of final causality among others.
(Contrary to a common misconception, final cause is NOT equivalent to "function" in the biological sense; such functions are just one special case of a more general phenomenon. What is essential to final causes is just directedness towards an end, something evident in every regular causal relation, however simple. For Thomists, the main reason to believe in final causality is that without it efficient causality of any sort becomes unintelligible, thus opening the way to e.g. the standard Humean puzzles. All of this is explained in detail in [Feser's book] The Last Superstition: A Refutation of the New Atheism.)
Feser points out the simplicity St. Thomas can see in nature. While Paley cites the designedness of a complex watch as evidence, St. Thomas' Fifth Way may cite any pattern. He uses the image of an archer guiding an arrow, but only by way of analogy.
Those of us still under the influence of mechanistic physics may hope that Feser's book further addresses how teleology still is observable in nature.