A saying is any concisely written or spoken linguistic expression that is especially memorable because of its meaning or structure.
There are a number of specific types of sayings:
Aphorism – A saying that contains a general, observational truth; "a pithy expression of wisdom or truth".Adage, proverb, or saw – A widely known or popular aphorism that has gained its credibility by virtue of long use.
Apophthegm – "[A]n edgy, more cynical aphorism; such as, 'Men are generally more careful of the breed of their horses and dogs than of their children.'"
Cliché or bromide – An unoriginal and overused saying.
Platitude – A cliché unsuccessfully presented as though it were truly meaningful, original, or effective.
Epigram – A clever and often poetic written saying that comments on a particular person, idea, or thing.
Epitaph – A saying in honor of a dead person, often engraved on a headstone or plaque.
Epithet – A descriptive word or saying already widely associated with a particular person, idea, or thing.
Idiom – A saying that has only a non-literal interpretation; "an expression whose meaning can't be derived simply by hearing it, such as 'Kick the bucket.'"Four-character idiom
Chengyu – Chinese four-character idioms
Sajaseong-eo – Korean form of four-character idioms
Yojijukugo – Japanese form of four-character idioms
Mantra – A religious, mystical, or other spiritual saying that is repeated over and over, for example, in meditation.
Maxim or gnome – (1) An instructional saying about a general principle or rule for behavior; or, simply, (2) an aphorism.
Motto – A saying used frequently by an individual person or group to concisely state their general outlook or intentions.
Quip – A clever or funny saying based on an observation.
Witticism – A saying that is clever, and also usually funny, notable for its form or style just as much as (or more than) its content.