In (Givón, 2013), the author makes the two following groupings:
Functionalism: rationalism, naturalness, universality, mentalism, innateness, emergence, evolution
Structuralism: empiricism, arbitrariness, diversity, externalism, input-dependence
Is it correct?
Also, it the grouping of "functionalism" also true for the Cognitive Linguistics framework (i.e. Lakoff, Langacker, Goldberg, Croft, Talmy)
Terminology
Rationalism :
Rationalism is the philosophical view that knowledge is acquired through reason, without the aid of the senses. Mathematical knowledge is the best example of this, since through rational thought alone we can plumb the depths of numerical relations, construct proofs, and deduce ever more complex mathematical concepts. We can even envision that someone locked in a room with no sensory experience whatsoever might still arrive at a sophisticated level of mathematical knowledge. Several ancient and medieval writers held to rationalism, most notably Plato and philosophers who followed in the Platonist tradition. In the mid seventeenth-century, though, rationalism was given a unique twist by philosophers who held that our most important mental concepts are innate, or inborn, and from these we deduce other truths with absolute certainty. Advocates of this position were largely from the continental European countries of France, the Netherlands, and Germany, hence this new breed of rationalism is often called “Continental Rationalism.” The main philosophers associated with this movement, which we will explore in this chapter, are René Descartes, Nicholas Malebranche, Baruch Spinoza, and Gottfried Wilhelm Leibniz. (Definition by Professor James Fieser, from the article "Continental rationalism", The History of Philosophy: A Short Survey)
Empiricism:
During the seventeenth and eighteenth-centuries, Britain certainly had its fair share of rationalist philosophers, particularly of the Platonist variety. However, Britain’s philosophy was soon dominated by an alternative and more scientific view that knowledge is gained primarily or mainly through the five senses. We see this presumption in Francis Bacon’s statement that in our efforts to understand nature we can “can act and understand no further than [we have] ... observed in either the operation or the contemplation of the method and order of nature” (New Organon, 1.1). Direct experience is foundational for obtaining knowledge, and this position is known as empiricism. During the first half of the 18th century, three great philosophers—Locke, Berkeley and Hume—argued for this approach, thus forming a philosophical movement known as British empiricism. Contrary to the 17th century rationalist philosophers in Continental Europe, these British empiricists largely denied the role of innate ideas and deduction in the quest for knowledge. Instead, they argued, knowledge comes from sensory experience and inductive reasoning. (Definition by Professor James Fieser, from the article "British Empiricism", The History of Philosophy: A Short Survey)
Direct comparison between empiricism and rationalism:
The empiricists solve [the problem of the origin of ideas] in a very different way than Descartes and his successors like Spinoza, Malbranche or Leibniz. Empiricists are interested in the how and not the why. Because the latter is, in their eyes, unattainable. (Jean-Michel Dufays, "L'empirisme dans les îles britanniques aux XVIIe et XVIIIe siècles", around 3rd minute, Translated from French)
As I understand it, this quote states that rationalists are motivated to find the why of phenomena, while the empiricists are motivated to find the how of phenomena.
I am not sure about the definition of mentalism and externalism. And I am not sure why to oppose naturalness to arbitrariness.
References:
Givón, T. (2013). On the Intellectual Roots of Functionalism in Linguistics. In Shannon Bischoff & Carmen Jany (eds.), Functional Approaches to Language, 9–28. Berlin, Boston: De Gruyter.