A proverb is a short pithy saying, expressing a folksy truth that is widely accepted, as in “A fool and his money are soon parted.”
An adage is a time-honoured widely known proverb that has become accepted as a truth, such as, “Actions speak louder than words.” (An old adage is a cliché.)
An aphorism is a short statement expressing a piece of wisdom, often wittily put. Aphorism implies depth of content and stylistic distinction: Few writers have coined more aphorisms than Benjamin Franklin has.
A maxim is a concise statement of a principle, a truth, or a rule of conduct, such as, “Neither a borrower nor lender be.”
A saying is an often repeated and familiar expression: a collection of philosophical sayings. The sayings of Confucius.
A motto differs from the maxim in that it merely states a guiding principle or belief rather than a precept. Mottoes are usually chosen by a group, an institution, a nation etc. as an expression of a purpose or ideal: “Be prepared “ is the motto of the Boy Scouts; “In God we trust” is the motto of the United States.
( Source: The American Heritage® Dictionary of the English Language, Fourth Edition)