Quotations  

Aphorism: A statement of some general principle, expressed memorably by condensing much wisdom into few words:  'Give a man a mask and he will tell you the truth' (Wilde); 'The road of excess leads to the palace of wisdom' (Blake).  Aphorisms often take the form of a definition:  'Hypocrisy is a homage page by vice to virtue' (La Rochefoucauld).  An author who composes aphorisms is an aphorist.  Adjective: aphoristic.

Maxim:  A short and memorable statement of a general principle; thus an aphorism or apophthegm, especially one that imparts advice or guidance.  The French writer La Rochefoucauld published his aphorisms as Maximes (1665), while Benjamin Franklin included several celebrated examples in his Poor Richard's Almanack (1733-58), including the maxim 'Three may keep a secret, if two of them are dead'.

Proverb:  A short popular saying of unknown authorship, expressing some general truth or superstition: 'Too many cooks spoil the broth."  Proverbs are found in most cultures, and are often very ancient.  The Hebrew scriptures include a book of Proverbs.  Many poets-notably Chaucer-incorporate proverbs into their works, and other imitate their condensed form of expression: William Blake's 'Proverbs of Hell' in The Marriage of Heaven and Hell (1793) are strictly speaking, aphorisms, since they originate from a known author.  Adjective: proverbial.

All entries from The Oxford Dictionary of Literary Terms.  Chris Baldick.  Oxford University Press. 2008.