Is there a scientific term for the sun burning out?

Answer 1

Red Giant effect:

When the primary fuel of the sun depleted, the fusion of 2H -> He stop at the core and the core contract. The surface is still burning but greatly expand with lower temperature from existing sun but a lot larger. Finally, when the sun really burn out it, the collapse remain mass become White Dwarf. All is part of stellar evolution.

Process of Sun burning is Nuclear Fusion Reaction, refer to it as burning usually make confuse that the sun is chemically burn and require oxygen.