What's the difference between a red giant and a red supergiant? I've seen both theoretical and observational definitions of stars. For example, an AGB star is a star where two sets of nuclear reactions (helium to carbon and hydrogen to helium) are taking place in shells around the core, and a super AGB star is one that is also burning carbon in the core.
Is there a similar theoretical distinction between red giants and red supergiants? I know RGB stars are burning hydrogen in a shell while the core is inert, so is a red supergiant a star which is also burning helium in the core (or something similar)?
 A: The short answer is no: there isn't a agreed theoretical distinction between red giants and red supergiants.
The source of confusion is that the red giant branch (RGB) is a theoretical concept, but the Yerkes spectral classification also defines a red giant observationally. So when
astronomers talk about red giants, it isn't necessarily clear which is meant. Scientists who calculate models of stars are probably talking about stars that are burning hydrogen in a shell around a helium core, whereas scientists who actually measure starlight are probably talking about stars which meet certain criteria for colour and brightness. The spectral classification defines red supergiants, but there isn't a corresponding theoretical "red supergiant branch" like there is for the RGB.
So, unlike red giants, red supergiants are simply bright, red stars. It so happens that they may be in the same evolutionary state, but it is also possible that they have moved on. For example, most massive stars will appear as red supergiants while helium is fused into carbon in the core.
