These phrases, which refer to the radio wavelength employed, are used in radio communications. There is no actual formal definition of longwave, however they are low frequency radio waves that are often below 540 kHz.
These low frequency radio waves travel across the earth via ground waves and may be picked up practically everywhere. On the other hand, shortwave radios encompass the spectrum from long or medium wave up to microwave frequencies and are higher frequency (hence shorter wavelength). Medium frequencies (HF) are a combination of ground and sky wave and may be received at medium to long ranges. Higher frequencies (VHF and UHF) are mostly short range sky wave propagation.