Dictionary definitions of all three are very similar, typically something like:
a pithy observation which contains a general truth
But the Wikipedia entries for each are quite different. Are these words largely interchangeable synonyms?
In the Wikipedia entry for adage, for example, a proverb is defined as an adage produced from folk wisdom, whereas an aphorism has "not necessarily gained credit through long use, but is distinguished by particular depth or good style".
It is common to find different words existing in English to represent a similar idea. It is an essential characteristic of a language with a long history.
To give you some idea: (I have linked the etymologies as well, which could give some idea about the original differences between the words which have deteriorated over time and use.)
Aphorism:
A ‘definition’ or concise statement of a principle in any science (OED)
This is essentially used to refer to a definition in science or any other technical education.
Adage:
A maxim handed down from antiquity (OED)
Any principle bequeathed from the past is an adage.
Proverb:
A short pithy saying in common and recognized use (OED)
A proverb has to be pithy and also common in use.
However we can certainly say that these distinctions in the definition are largely ignored in practical usage. Along with these three words, others like saw, maxim and apothegm could also be used interchangeably. Proverb, adage and maxim are the commonest from what I have encountered.
You could say that an aphorism is a perverse or paradoxical proverb; a corrective for experience. Auden says they're an aristocratic genre of writing (Viking Book of Aphorisms). Hollingdale in his introduction to Lichtenberg Aphorims says they’re ‘philosophical,’ while epigrams are not, and they have the impact of the punch line of a joke, For example:
There are truths that go around so dressed up you would take them for lies, but which are pure truths none the less.
The world offers more correction than consolation.
God who winds up our sundials.
Georg Chrisotoph Lichtenberg
A proverb is “a short pithy saying in common use, a concise sentence, which is held to express some truth ascertained by experience or observation and familiar to all.” Shorter Oxford English Dictionary.
Webster’s Second: A proverb is an adage couched usually in homely and vividly concrete phrase; as, “accused (in the phrase of a homely proverb) of being ‘penny-wise and pound-foolish' The Spectator".
"An adage is a saying of long-established authority and universal application," Webster's Second. Shorter Oxford shows "adagial" - maybe similar to "proverbial"? and cites Lady Macbeth, 'And live a coward in thine own esteem, Letting “I dare not” wait upon “I would” Like the poor cat i’ the adage?'
An apothegm is “a terse, pointed saying embodying an important truth in a few words,” Shorter Oxford; “a terse and sententious aphorism,” Webster’s Second
Liddell & Scott say of the Greek apophthegm, “to speak one’s opinion plainly; metaphorical of vessels when struck.”
A saying "is a brief current or habitual expression of whatever form," Webster’s Second.
Used casually, they are all synonyms. Used specifically, they are closely related with slight differences and occasional overlapping meanings.
This is my simplified understanding of these related terms from the definition of Saying from Wikipedia.
(My) Examples:
Something I noticed reading in Wikipedia that I have not seen mentioned in your posts is that an aphorism is a an "original" statement. That alone seems to help easily distinguish it among the others. Example: Carpe diem... which is original in that we know the author of the statement was Horace from the poem Odes 23 BC. But it is short, concise, memorable, from antiquity, commonly used and understood broadly even though it is still quoted in its original language. It is formal and philosophical, yet practical. I think it could fit all the categories that we have been discussing. What do you think?
Wikipedia's "Saying" article includes the following brief defintions of the three terms you mention:
Aphorism – A concise definition, notably memorable.
Adage – An aphorism that has gained credibility by virtue of long use.
Proverb – An expression of practical truth or wisdom.
The three words are not interchangeable, in that a given saying might qualify for one or two of the categories but not the others. For example, proverb "You can lead a horse to water, but you can't make him drink" may also be termed an adage, but does not rise to the level of aphorism.
The most concise statement of differences I've seen is from Wikipedia's "Adage" article:
Some adages are products of folk wisdom that attempt to summarize some of the basic truth; these are generally known as proverbs or bywords. An adage that describes a general rule of conduct is a "maxim". A pithy expression that has not necessarily gained credit through long use, but is distinguished by particular depth or good style is an aphorism, while one distinguished by wit or irony is an epigram.
I dispute! Most of these are only vaguely similar. In many cases there is one or more key features which set each apart from the others.
A "saying" is any (vaguely) memorable words. They could have a moral, ethical, or educational focus, or could be something radically different. "The rain in Spain falls mainly on the plain" is a saying to aid pronunciation - its actual content is irrelevant. "She sells sea shells by the sea shore" is designed to be a tongue-twister, deliberately created for people to fail to pronounce it correctly. A saying could be long or short, common or obscure, full of wisdom or total gibberish.
An "aphorism" is a phrase explaining or extolling a truth. That truth is in general universal and rarely disputed.
An "axiom" is a simple declared fact or assumption, from which more complicated deductions can be developed. It is a base-line starting point. Its truth may be challenged, but only from the context of a new and separate line of thought. "Every human has the right to life" is a generally-accepted 21st century axiom, on which (for example) national murder laws are built.
An "adage" or "proverb" is "folk wisdom" - short, formulaic (that is, there's deemed to be one "correct" way to say it in any given language), yet the wisdom is only applicable in specific situations. "Make hay while the sun shines", "a stitch in time saves nine", and so on are extremely situational, and many proverbs actually have a matching proverb that suggest the opposite wisdom. "Strike while the iron is hot" suggests people should act swiftly and decisively, whereas "better safe than sorry" is one extolling caution.
A "catechism" is a summary or exposition of doctrine, most particularly in Catholicism. It is global and directional. "Do unto others as you would have them do unto you" is a catechism - it is a directive (an instruction) from Jesus to the disciples, and hence a directive from the Church to the believers.
A "motto" is a simplified or summarizing phrase to capture a value or mission or a person or group. Where the intent of a catechism is clear, a motto may need interpretation. "Just do it", "Semper Fidelis", "Mens sana in corpore sano" are all example mottos that are touchstones reminding members of the values of their organisations, and in many cases excellent advertising fodder. Mottos are publicly displayed, particularly in coats of arms, business logos, and the like, whereas catechisms are generally not.
A "maxim" is not a saying, but a personal values brief. Of all the catechisms a person may focus on, a given person may adopt "do unto others as you would have them do unto you" as their key to guide their personal actions and decisions on a regular basis. That person has thus taken the (global) catechism on as their (personal) maxim, by putting the catechism into action. "Semper Fidelis" might be a maxim to a given person, if it is actually put into action by that person.
An "idiom" is making an unusual comparison to make a point. As the above answer mentions "raining cats and dogs" is not literal, but the conjured image gives an indication of the true intensity of the rain. Idioms are generally difficult to understand to people with literal thinking patterns.
A "quote" is simply a direct saying from an individual person or source, recorded exactly as spoken or written. It too could be long or short, wise or foolish, boring or entertaining.
Confusion may arise when given phrases are used with different intents (or mis-intent). Example: "So in everything, do to others what you would have them do to you, for this sums up the Law and the Prophets."
[moved from duplicate]
Well, let's see ...
"Adage" is how old that commercial is on a cable TV channel. "Aphorism" is a word that comes before ('afore) another word. "Epigram" is a drawing on your epidermis (ie, a tattoo). "Maxim" is the largest of several numbers. "Apothegm" is that engagement ring you bought in a drug store.
And "proverbs", of course, help us all to be better Mouseketeers.
