"Ironic" = say one thing but mean it in a different way, in a funny way. "Satirically" = to make intentionally fun of something in a style called "satyre". "Satyre" is a kind of humor, a kind of comedy art, from ancient Greece with very strict rules for something being "satyrical".

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Ironic situations are those situations that are funny because things happen in a completely opposite way of what you expected. Satire on the other hand, is making fun of people- imitating them by exposing their flaws. ( ex. stupidity)