The trailier has it backwards. Retarded started as medical term (as did idiot) and then moved into popular usage.

From wikkipedia:

It was previously used as a medical term. The verb "to retard" means to delay or hold back, and so "retard" became known as a medical term in the late 19th and early 20th centuries to describe children with intellectual disabilities, or retarded mental development.[5] Until the 1960s, the terms moron, idiot, cretin, and imbecile were all genuine, non-offensive terms used, including by psychiatrists, to refer to people with mental intellectual disabilities and low intelligence. These words were discontinued in that form when concerns arose that they had developed negative meanings, with "retard" and "retarded" replacing them.[6][7] After that, the terms "handicapped" (United States) and "disabled" (United Kingdom) replaced "retard" and "retarded". Disabled is now considered a more polite term than handicapped in the United States as well.

TLDR:

Retard, moron, idiot, cretin, and imbecile were all once medical terms that morphed into slurs when adopted in general usage.