An adage is a short, memorable, usually philosophical saying. These kinds of saying go by any number of other names, and though there are probably distinctions, they seem pretty similar to me. For example, aphorisms, proverbs and bywords are close synonyms.
I did find that an adage that describes a general moral rule is usually called a "maxim". An aphorism seems to be more of an expression that seems "deep" and may not be widely used. But, one that is witty or ironic seems to get the tag "epigram".
Many adages are ancient and if they have been overused, they may be referred to nowadays as a "cliché", "truism", or "old saw."
Some more modern adages get labeled as "laws" or "principles," such as Murphy's Law.
The word "aphorisms" comes from a book by that name by Hippocrates that is a series of propositions concerning the symptoms and diagnosis of disease and the art of healing and medicine. The first line is "Life is short, art long, opportunity fleeting, experience deceptive, judgment difficult."
I found many lists of adages online that are very common, such as "Don't count your chickens before they hatch" and "Don't burn your bridges."
I was surprised to find how many adages come to us from the Dutch humanist Desiderius Erasmus Roterodamus, commonly known as simply Erasmus. He didn't create these. He compiled them. He published several volumes with the final edition of Adagia (1536) having more than 4,000. Most of them are annotated Greek and Latin proverbs that he compiled.
Here's a sampler of ones (translated to English) that you are likely to recognize:
More haste, less speed
The blind leading the blind
A rolling stone gathers no moss
One man's meat is another man's poison
Necessity is the mother of invention
One step at a time
To be in the same boat
To lead one by the nose
A rare bird
Even a child can see it
To have one foot in Charon's boat (To have one foot in the grave)
To walk on tiptoe
One to one
Out of tune
A point in time
I gave as bad as I got (I gave as good as I got)
To call a spade a spade
Hatched from the same egg
Up to both ears (Up to his eyeballs)
As though in a mirror
Think before you start
What's done cannot be undone
Many parasangs ahead (Miles ahead)
We cannot all do everything
Many hands make light work
A living corpse
Where there's life, there's hope
To cut to the quick
Time reveals all things
Golden handcuffs
Crocodile tears
To lift a finger
You have touched the issue with a needle-point (To have nailed it)
To walk the tightrope
Time tempers grief (Time heals all wounds)
With a fair wind
To dangle the bait
Kill two birds with one stone
To swallow the hook
The bowels of the earth
Happy in one's own skin
Hanging by a thread
The dog is worthy of his dinner
To weigh anchor
To grind one's teeth
Nowhere near the mark
To throw cold water on
Complete the circle
In the land of the blind, the one-eyed man is king
No sooner said than done
Neither with bad things nor without them (Women: can't live with 'em, can't live
without 'em)
Between a stone and a shrine (Between a rock and a hard place)
Like teaching an old man a new language (Can't teach an old dog new tricks)
A necessary evil
There's many a slip 'twixt the cup and the lip
To squeeze water out of a stone
To leave no stone unturned
Let the cobbler stick to his last (Stick to your knitting)
The cart before the horse
Dog in the manger
One swallow doesn't make a summer
His heart was in his boots
To sleep on it
To break the ice
Ship-shape
To die of laughing
To have an iron in the fire
To look a gift horse in the mouth
Neither fish nor flesh
Like father, like son
This appeared earlier on Weekends in Paradelle.