  Fast radio bursts (FRBs) are bright milliseconds radio transients with large
dispersion measures. Recently, FRB 200428 was detected in temporal coincidence
with a hard X-ray flare from the Galactic magnetar SGR 1935+2154, which
supports that at least some FRBs are from magnetar activity. Interestingly, a
portion of X-ray flares from magnetar XTE J1810-197 and the Sun are also
accompanied by radio bursts. Many features of Galactic FRB 200428 and
cosmological FRBs resemble solar radio bursts. However, a common physical
origin among FRBs, magnetar radio pulses and solar radio bursts has not yet
been established. Here we report a universal correlation between X-ray
luminosity and radio luminosity over twenty orders of magnitude among solar
type III radio bursts, XTE J1810-197 and Galactic FRB 200428. This universal
correlation reveals that the energetic electrons which produce the X-ray flares
and those which cause radio emissions have a common origin, which can give
stringent limits on the generation process of radio bursts. Moreover, we find
similar occurrence frequency distributions of energy, duration and waiting time
for solar radio bursts, SGR 1935+2154 and repeating FRB 121102, which also
support the tight correlation and the X-ray flares temporally associated with
radio bursts. All of these distributions can be understood by avalanche models
of self-organized criticality systems. The universal correlation and
statistical similarities indicate that the Galactic FRB 200428 and FRBs seen at
cosmological distances can be treated as scaled-up solar radio bursts.
