The specific epithet for this taxon, carnosus, translates to “fleshy”, in this case referring to the thick petals. The common name, fleshy-flowered spindletree, obviously mirrors the scientific name.
The genus Euonymus belongs to the family Celastraceae. Browsing through the listing of other genera in the family, I feel confident in stating it is one of the few members of the Celastraceae to succeed in adapting to temperate climates.
Photography resource link: The plant images of Wikimedia contributor Stan Shebs. Many photographs from UBC Botanical Garden are in the gallery, including this one of today’s plant, Euonymus carnosus. It’s a rather good illustration of the thickened petals!