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Moron is a term once used in psychology and psychiatry to denote mild intellectual disability. The term was closely tied with the American eugenics movement. Once the term became popularized, it fell out of use by the psychological community, as it was used more commonly as an insult than as a psychological term. It is similar to imbecile and idiot.
In typical usage, retard (pronounced /ˈɹiː.tɑːɹd/, REE-tard) is a slur for someone who is considered stupid, slow to understand, or ineffective in some way as a comparison to stereotypical traits perceived in those with intellectual disability. The adjective retarded is used in the same way, for something very foolish or stupid. The word is sometimes censored and referred to as the euphemistic "r‑word" or "r‑slur".
Retard 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. For context, 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. 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. This trend was dubbed a "euphemism treadmill" by Steven Pinker.