Is a metaphor a type of analogy?

Strictly, no. A metaphor is a trope (a figure of meaning, where one word stands for something other than itself), and an analogy is a mode of reasoning by structural similarity; they sit on different axes, not on a parent-child line. The wrinkle: Aristotle's own taxonomy of metaphor, in Poetics 21, names one of its four sub-kinds "metaphor by analogy," the four-term proportion A:B::C:D, as in "old age is the evening of life." So the categories overlap at exactly one well-defined corner, and most of the confusion about whether one contains the other comes from people pointing at that corner and disagreeing about what it means.

What's the working test?

For any single sentence, the figure usually announces itself by what it asks the reader to do.

A metaphor swaps one thing for another and lets the reader infer the mapping. "All the world's a stage, / And all the men and women merely players" (Shakespeare, As You Like It, 1623, II.vii). The world is not declared like a stage; it is called one, and the reader does the rest.

An analogy spells the mapping out, usually with explicit relational structure. "Just as the eye is the lamp of the body, so is the mind the lamp of all knowledge" extends the comparison and points at the structure being mapped. The reader is not asked to feel an equivalence so much as to follow it.

The test, then: if the sentence wants the reader to feel the swap, it is leaning metaphor; if it wants the reader to follow a proportion across to understand something else, it is leaning analogy. The heuristic of "feeling vs. thinking" is useful as long as you remember it is a heuristic, not a definition.

Example	Metaphor or analogy?	Why the test points there
"All the world's a stage" (Shakespeare, As You Like It, 1623)	Metaphor	One term is swapped for another with no explicit comparison. The reader infers the mapping (people are players, lives are scenes) on their own.
"A nation is like a ship: every man is on board, and if it sinks, every man goes down with it" (paraphrased from Lincoln's Civil War correspondence, 1862)	Analogy	The structure is spelled out. The comparison rides on an explicit "is like," and the relational point (shared fate) is the reason for the comparison.
"Old age is the evening of life" (Aristotle, Poetics, 21)	Metaphor by analogy	The sentence reads as a metaphor (one term swapped for another), but the swap is licensed by a proportion: old age is to life what evening is to day. The four-term structure is exactly what Aristotle classifies as analogical metaphor.

The borderline row is the one to remember. A metaphor can be built on an analogical structure underneath; that does not make every metaphor an analogy, and it does not make analogy a category that contains metaphor.

Why some writers say metaphor is a type of analogy

The claim that metaphor sits inside analogy is defensible, and a reader will meet it. It comes from two traditions that do not quite say the same thing.

The first is Aristotle, Poetics, chapter 21. He divides metaphor into four kinds by the basis of the swap: genus to species, species to genus, species to species, and proportion (analogy). The proportional kind, metaphora kat' analogian, works on the four-term ratio A:B::C:D. Aristotle's own example is "the shield of Dionysus" for a wine cup, because the wine cup is to Dionysus what the shield is to Ares. The proportion licenses the swap. On Aristotle's taxonomy, then, one of the four sub-kinds of metaphor is analogical; that is a real overlap, but a narrow one. He is classifying metaphor by what the substitution is based on, not arguing that metaphor is a subspecies of analogy at large.

The second is cognitive science. Dedre Gentner argues in "Metaphor Is Like Analogy" (2001) that metaphor is best modeled as a special case of analogical mapping: the reader (or hearer) comprehends a metaphor by aligning relational structure across two conceptual domains, source and target. On this view, Juliet is the sun is processed by mapping the relations that hold of the sun (warmth, centrality, the thing the world is organized around) onto Juliet. Gentner is not making a claim about rhetorical taxonomy; she is modeling comprehension. Her "metaphor is a kind of analogy" runs at the level of cognitive process, not at the level of how a handbook of figures classifies tropes.

So: under the Aristotelian sub-taxonomy and the Gentner-style cognitive model, yes, there is a real sense in which metaphor draws on analogical structure. Under the standard rhetorical-figures taxonomy, no, a metaphor is not a subtype of analogy. Those two answers belong to different questions, and reading them as the same answer is where most of the confusion starts.

Did you know? Aristotle's example of metaphor by analogy in the Poetics (21) is "the shield of Dionysus" for a wine cup, because the wine cup is to Dionysus what the shield is to Ares. The proportion A:B::C:D is what licenses the swap. Two and a half thousand years on, the four-term ratio is still the cleanest test for whether a given metaphor is the analogical kind.

Why most rhetoric handbooks keep them separate

The counterweight comes from the working taxonomy of rhetorical figures. In that tradition, a metaphor is a trope: a figure of meaning, where a word is used in a sense other than its literal one. Analogy is generally not classed as a figure of speech at all. It is a mode of reasoning or explanation that uses structural similarity, often spanning multiple sentences or a whole paragraph. Tropes are local: they live inside a sentence. Analogies are extended: they live across one.

The standard references on the figure side make this division explicit. Edward P. J. Corbett's Classical Rhetoric for the Modern Student treats metaphor among the tropes and treats analogy as an argumentative move (alongside induction and example), not a figure. The Silva Rhetoricae taxonomy assembled by Gideon Burton lists metaphor under tropes of meaning; analogy appears as a method of argument and proof, not in the figure inventory. The split is consistent across the handbook tradition because the categories are answering different questions: tropes are about how a single word or phrase carries meaning; analogies are about how one set of relations can be used to explain another.

The two frames are not actually in contradiction. Metaphor draws on analogical structure (the Aristotle and Gentner observation) and metaphor is a trope, analogy is reasoning (the handbook taxonomy) are different cuts at the same material. The first describes what is going on cognitively when a metaphor lands; the second describes how to file the move in a reference work. A working writer can hold both. By default, treat metaphor and analogy as adjacent but distinct; reach for "metaphor by analogy" specifically when the swap rides on a four-term proportion you can write out.

Where does this leave simile?

Simile is the third figure on the same map, and it is usually the next one a writer asks about. A simile is a figure of comparison that marks the comparison explicitly with like or as: "My love is like a red, red rose" (Burns, "A Red, Red Rose," 1794). The marker is the defining feature. Drop the like and the same sentence becomes a metaphor.

In mechanism, simile is closer to analogy than metaphor is. Both simile and analogy lay the comparison out for the reader; metaphor compresses it. Many extended analogies are built out of similes ("a heart is like a pump, with valves that work in the following ways…"), with each clause spelling out one element of the mapping. The progression from simile through analogy to metaphor runs roughly from most explicit to most compressed.

A three-way orientation worth keeping in mind. Metaphor: one thing is another, the swap implicit. Simile: one thing is like another, the swap explicit. Analogy: one structure maps onto another, the mapping spelled out across more than a single phrase. The clean test for whether a sentence is metaphor or simile is whether like or as appears: present, simile; absent, metaphor. On the metaphor and analogy side, the precise line between an analogy and a metaphor lives in whether the sentence compresses the comparison into a single term or extends it across a structure.

When you are staring at a single sentence in your own draft, the taxonomy is not the question you have to settle. The question is which word to use, and the test is the takeaway: does the sentence swap one thing for another, or does it map a structure across to explain? Settle that, and the rest is filing.