The pillar defines the three classical modes. This page does what a definition can't: it points all three at the same subject so you can feel the difference in aim, not just in description.
The subject: a tech CEO who keeps promising that artificial intelligence will free humanity from drudgery, while quietly laying off the people who did the drudgery.
Horatian treats him as a familiar comedy. The piece is fond, almost affectionate — it casts him as a man who has confused a keynote for a personality and genuinely believes his own slide deck. The laugh is recognition: we've all met him. The correction is gentle; we're not asked to hate him, only to see how silly the posture is.
Juvenalian treats him as a crime. Same CEO, but the piece refuses to find him charming. It sets the layoff numbers beside the stock buyback, the "freeing humanity" language beside the severance terms, and lets the contrast indict. The tone is cold. There's no fond chuckle, because the Juvenalian satirist believes something real was done to real people, and a joke that softened it would be a betrayal.
Menippean ignores the man almost entirely and goes after the belief — the cultural faith that technological progress is automatically moral, that efficiency is a virtue, that the future is a product. The piece might be a fake oral history from 2075, a glossary of invented corporate terms, or a dialogue between a chatbot and the ghost of a factory worker. It's stranger, harder to summarize, and aimed at the shared illusion that made the CEO possible in the first place.
Notice what changes across the three: the facts can stay identical. What moves is the altitude of the target. Horatian aims at the person and likes him. Juvenalian aims at the person and convicts him. Menippean aims past the person at the idea he's a symptom of.
That's why "what type is it?" is more useful than it sounds. It tells you what the writer wants from you — a knowing smile, a clenched jaw, or the disorientation of watching solid ground turn out to be a story everyone agreed to believe. Most strong satire mixes modes, but one usually dominates, and naming it tells you where the writer thinks the real problem lives.