"Tu pui paltonul pe cuier."

Translation: You put the coat on the rack.

[RussJenkins]

Is it the same word of "rack" and "hanger" they seem very different things?

[crbratu]

"Cuier" is something you hang clothes to. The simplest form would be a nail in the wall ("cui" = "nail") . The hanger having the shape of the shoulders is called "umeraș" ("umăr " = "shoulder ")