A phrase that's short, catchy, and clever can be described as gnomic. Your grandmother's famous gnomic aphorisms include "Pet a cat and you've got a job for life!"

The root of this word is the Greek gnome, "an opinion." Ancient Greeks had an entire genre devoted to what they called gnomes (today generally referred to as gnomic poetry): pithy, meaningful phrases that rhymed. Gnomic verse started out expressing strong moral and religious opinions. These gnomes have evolved into truisms and adages that are easy to remember but not always widely understood, like the gnomic idea that "a penny saved is a penny earned."

Definitions of gnomic
  1. adjective
    expressed in or relating to short, pithy statements or maxims
    gnomic verse”
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