What does "order" mean in this context?

Solution 1:

Botanical nomenclature is based on a hierarchy of ranks. Wikipedia gives a succinct summary of the hierarchy:

Wikipedia

the order (Latin: ordo) is

a taxonomic rank used in the classification of organisms and recognized by the nomenclature codes. The well-known ranks in descending order are: life, domain, kingdom, phylum, class, order, family, genus, and species, with order fitting in between class and family. An order contains various plant families, each containing genera, each containing species.

enter image description here

Fumariaceae is a family of plants contained in the order Ranunculares

Families of Angiosperms

Fumariaceae:

Taxonomy. Subclass Dicotyledonae; Crassinucelli. Dahlgren’s Superorder Ranunculiflorae; Ranunculales. Cronquist’s Subclass Magnoliidae; Papaverales. APG III core angiosperms; peripheral eudicot; Superorder Ranunculanae. APG IV Order Ranunculales.

Corydalis is a genus in the family Papaveraceae, in the order Ranunculales.

Wikipedia

The Papaveraceae are an economically important family of about 42 genera and approximately 775 known species[3] of flowering plants in the order Ranunculales

Hence, Darwin is referring to controversy with Treviranus about the order Ranunculales, which contains his examples - of the family Fumariacae and the genus Corydalis (a member of family Papaveraceae).

Here is my attempt to summarize all this. Darwin had in mind the order Ranunculales, which contains the particular family and genus that he mentioned (both in red):

enter image description here