Similarity is a relation, more or less formal, depending on context. We naturally associate similar things, as in rhyming; and especially as having similar uses, for need detects likeness: necessity is the mother of resemblance. Euclidean geometry, which is much concerned with shape, does away with “similarity” in the general sense, narrowing its meaning to mere “sameness of shape.” In certain contexts, as with words and living things, it is “relatedness” that can be reduced to a fairly precise meaning: “relation by descent,” which can (as a rule, in principle) be exactly diagrammed. Without losing the useful breadth of “similarity” in these contexts—admitting, therefore, such categories as appearance, sound, shape, function, behavior—one can try to limit it to refer to properties which can be measured. In the case of living things, the modes of classification by (familial) relatedness and (measurable) similarity have respectively been given the unlovely names of cladistics (referring to branching of a genealogical tree) and phenetics (referring to appearance).
In Chapter 13 of The Origin of Species Darwin writes,
It might have been thought (and was in ancient times thought) that those parts of the structure which determined the habits of life, and the general place of each being in the economy of nature, would be of very high importance in classification. Nothing can be more false. … It may even be given as a general rule, that the less any part of the organisation is concerned with special habits, the more important it becomes for classification. … [A]lmost all naturalists lay the greatest stress on resemblances in organs of high vital or physiological importance. … But their importance for classification, I believe, depends on their greater constancy throughout large groups of species; and this constancy depends on such organs having generally been subjected to less change in the adaptation of the species to their conditions of life. … [D]ifficulties in classification are explained … on the view that the natural system is founded on descent with modification; that the characters which naturalists consider as showing true affinity between any two or more species, are those which have been inherited from a common parent, and, in so far, all true classification is genealogical. … We have no written pedigrees; we have to make out community of descent by resemblances of any kind. Therefore we choose those characters which, as far as we can judge, are the least likely to have been modified in relation to the conditions of life to which each species has been recently exposed. … On my view of characters being of real importance for classification, only in so far as they reveal descent, we can clearly understand why analogical or adaptive character, although of the utmost importance to the welfare of the being, are almost valueless to the systematist. For animals, belonging to two most distinct lines of descent, may readily become adapted to similar conditions, and thus assume a close external resemblance; but such resemblances will not reveal—will rather tend to conceal their blood-relationship to their proper lines of descent.
“True classification,” he believes, is by relatedness. Related does not imply similar, because organs of related creatures may become different through modification under different conditions—species may diverge. Birds and crocodiles are fairly closely related, but quite dissimilar. Similar does not imply related, because organs of unrelated creatures may become alike by modification under like conditions—species may converge. Many marsupial (Australian) mammals have similar placental counterparts, to which they are very distantly related.
We naturally—naively, in a pre-Darwinian condition—classify by similarity, as we perceive it. This is useful: it would not profit us to associate bird and crocodile; it would profit us to show the same respect to gray as to Tasmanian wolves (while the latter existed). Grouping creatures in this way, we are behaving like the rest of the natural world, which can only act on those characteristics of any organism which it notices (understanding “notice” in the widest sense). Then if divergence or convergence leads us to misjudge relatedness, the cause of our error is essentially the same as what makes it an error. We go wrong by relying on noticeable features; those features mislead just because they are noticeable, hence were liable to evolutionary modification.
After Darwin, we may choose to classify by relatedness, if we can; and molecular detail enables the choice. Have we stepped out of Nature? On the whole, no, since most biological investigation continues to aim at the advantage of our insatiable species.