The practical difference
A red giant is an expanded later-life star like the future Sun. A red supergiant is the expanded later-life form of a much more massive star.
That starting mass changes everything: luminosity, internal pressure, fusion stages, lifetime, and final remnant.
Why they can be confused
Both can be cool and reddish. Both can have bloated atmospheres. But a red supergiant is usually larger, brighter, and less dense at its outer layers.
The name supergiant also refers to luminosity class, so classification depends on spectra as well as size.
Different endings
A red giant like the future Sun sheds outer gas and leaves a white dwarf. A red supergiant can develop an iron core and collapse.
That collapse can power a supernova and leave a neutron star or black hole.
Giant vs supergiant: what is the difference?
An ordinary giant has expanded beyond the main sequence, but a supergiant occupies the much more luminous class I region of stellar classification. Supergiants also have lower surface gravity and commonly come from more massive stars.
Radius alone is not enough to separate the classes. Astronomers compare spectra, luminosity, temperature, mass, and evolutionary context.