Classification bulked so large in the 18th Century that we ought to note what happened to it in the 19th. It underwent a metamorphosis, and retired to a supporting role.
The change from the classical period was heralded by the introduction of a new criterion for regarding a feature (of an animal or plant) as a character or index of taxonomic category membership.
In the Classical period proper, the criteria had been restricted to "the domain of the visible". After the revolution, the principle appealed to became organic structure.
On the new conception you can have two animals which have similar (and even identical) internal functional organisation, but which, to observation of the inspectable configurations of their parts, are dissimilar.
Likewise you may find inspectable similarities and functional differences.
So two results as far as classification is concerned:
1) you have a new respect in which things can resemble each other:
functional organisation. (New importance to function de-emphasises appearance.)
and
2) two levels: what is inspectable is determined by the underlying
organisation.