According to this post:
Mathematicians have a habit of hijacking common nouns and adjectives for mathematical objects and properties, sometimes with good reasons such as geometric or other analogies or metaphors, and sometimes arbitrarily. Just look at "group", "ring", "space", "sheaf", "atlas", "manifold", "field" and so on.
In fact, the term "regular" for finite-state languages, while still prevalent in automata theory, is not used very much in its algebraic cousin, finite semigroup theory or abstract algebra in general. Why? Because the term was already taken for a semigroup that is close to a group in a specific technical sense, so you couldn't match up a regular language in Kleene's sense with a corresponding regular semigroup. Third, Kleene defined another kind of event called "definite", which was much studied for a while, but has turned out to be not particularly fruitful. Today, finite sets of language play the role of definite events as the basis for regular events.
The preferred term in algebra is "rational" for both Kleene's class of languages and the more general semigroups and monoids. That usage also reflects an important analogy between the term "rational" in algebra as the solution of a linear equation with integer coefficients and the concept of rational power series in automata and formal language theory.
But what about the "regular" in "regular expression"? Does that also have the same terminology?
