These two words are synonyms that have a lot of overlap. Here is a list of similar words from the American Heritage Dictionary.
SYNONYMS saying, maxim, adage, saw, motto, epigram, proverb, aphorism. These nouns refer to concise verbal expressions setting forth wisdom or a truth. A saying is an often repeated and familiar expression: a collection of philosophical sayings. Maxim denotes particularly an expression of a general truth or a rule of conduct: “For a wise man, he seemed to me … to be governed too much by general maxims” (Edmund Burke). Adage applies to a saying that has gained credit through long use: a gift that gave no credence to the adage, “Good things come in small packages.” Saw often refers to a familiar saying that has become trite through frequent repetition: old saws that gave little comfort to the losing team. A motto expresses the aims, character, or guiding principles of a person, group, or institution: “Exuberance over taste” is my motto. An epigram is a witty expression, often paradoxical or satirical and neatly or brilliantly phrased: In his epigram Samuel Johnson called remarriage a “triumph of hope over experience.” Proverb refers to an old and popular saying that illustrates something such as a basic truth or a practical precept: “Slow and steady wins the race” is a proverb to live by. Aphorism, denoting a concise expression of a truth or principle, implies depth of content and stylistic distinction: Few writers have coined more aphorisms than Benjamin Franklin.