Idiom goes to a phrase's meaning not resulting from the ways normal words are put together with standard grammar. The phrase develops a meaning at odds with the compositional meaning of the words and typically has trouble being subjected to grammatical modification. "Let the cat out of the bag" doesn't regularly allow "the cat, let out of the bag by accident ...". No actual cat, no actual bag, and it's hard to see the analogy in the idiom. "Let the cats out the bag" suddenly becomes starkly literal. Even a construction like "the PR firm thought long and hard on the right marketing approach to letting the cat out of the bag about their client's new product." Typically the phrase entails accident or mistaken revelation, or at the very least information that was kept secret. You don't see that in the compositional meaning of the words "let, cat, out of, bag." And the use of the article is strange there, as well: We expect there to be a singular cat in the context, the cat to be prototypical, or to be old information in the narrative. It's an idiom. (Could be a cliche, if it's overused.)
"A stitch in time saves nine" was a cliche and is an aphorism. Cliche status depends on frequency. "We need to leverage our synergies" became a cliche. It's not an idiom nor an aphorism. Just a set phrase.
Other aphorisms are far from being cliches: Many a mickle makes a much. If it's not overused, it's probably not a cliche. Most probably haven't ever heard that aphorism. It's not an idiom; a mickle is a small quantity of something, and if you have a lot of small quantities you have a lot, or "much." It's strictly compositional.
Others "cliches" at the site are neither: "As many Chins as a Chinese phonebook" might be a cliche for some, but not for me. I've heard it perhaps once. A lot of people just want to participate and suggest any set phrase.
So we have a definition thing. Not that definitions in the least matter, so if you blather to kitty beyond random baiting, ethos rags subordinate. Then again, I suspect most would think definitions matter when it comes to words they think important.
The sample makes no claim to being random or adjusted by population, so I find the astonishment at having a bias in a biased sample to be astonishing.
Moreover, the attributions aren't always correct. "Ashes to ashes, dust to dust" is from the Anglican funeral service. "As ye sow, so shall ye (also) reap" is slightly paraphrased KJV (Britain, 1611), and is the same in the earlier Tyndale version. Not just a biased sample, but an unvetted sample. Perhaps I should list "he's the periphrastic antithesis of demotivational supercedent priorities" as a cliche.
This is Internet flotsam that should never become jetsam. May it sink and be derelict.