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."