A simili argument, Lat. similis, “similar, looking like, identical”.
Per analogiam argument, Lat. analogia, “resemblance, analogy”.

Perelman defines the argument a simili or “by analogy” as follows:

A legal proposition being given, which affirms a legal obligation relative to a subject or a class of subjects, this same obligation exists with regard to any other subject or class of subjects having with the first subject (or class of subjects) sufficient analogy so that the reason which determined the rule with respect to the first subject (or class of subjects) is valid with respect to the second subject (or class of subjects). Thus, the fact of having forbidden a traveler to climb on the steps accompanied by a dog leads us to the rule that it is also necessary to forbid it to a traveler accompanied by an equally inconvenient animal. (1979, p. 56)

By application of the a fortiori rule, travelers may be accompanied by a “less inconvenient” animal than a dog (maybe a cat?)” but not by a more inconvenient animal (a goat?)

As the extension clause “an equally inconvenient animal” shows, the a simili argument is based on categorization mechanisms. It covers the same kind of reasoning as a pari, and the rule of justice.
The terminology seems somehow redundant, S. Analogy; Genus.