As a baby, a lionfish has long, flowing pectoral fin rays that are individually sheathed (covered by a thin clear membrane). The dark spots are there to mimic eyes and confuse its prey. As the lionfish grows, both the sheath and the eyespots disappear, and its fins become proportionately smaller than the rest of its body. Its coloration also changes.
What other differences do you see?
Lionfish are venomous (unlike sea hares) and they use spines to inject their toxin. Their sting causes extreme discomfort to humans and can result in death.
Recent reports have stated that the stomach contents of lionfish can include other lionfish. In the absence of food, lionfish will resort to cannibalism and eat each other (meanwhile, sea hares would probably just shrink and starve to death, but I don’t plan on testing this).