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.