US Certification standards refer only to an "Aircraft Flight Manual" (AFM) and AFM's are only found in large or turbine aircraft.
Until 1976 light aircraft did not have to have any kind of manual as long as there was cockpit placards that stated the aircraft limitations and important speeds.
In 1976 the General Aviation Manufacturing Association (GAMA), came up with a standardized aircraft manual format and called it the "Pilot Operating Handbook".
It was model and serial number specific and became a required document. The POH format was adopted by most but not all American aircraft manufacturers.
Of note pilot shops sell copies of POH but they are titled "Information Manual" not POH. They are not serial number specific and can't be used as a replacement for the manufacturer issued POH.