An aphorism is a cleverly or wittily expressed piece of wisdom.

A dictum is an authoritative statement of a (supposed) truth.

These are aphorisms, but they are not dictums:

"Marriage is popular because it combines the maximum of temptation with the maximum of opportunity."--George Bernard Shaw

"Moderation is a fatal thing. Nothing succeeds like excess."--Oscar Wilde

These are dictums, but they are not aphorisms:

"Red wine with meat, white wine with fish."

"Never draw to an inside straight."