Most stars swell into giants when their core hydrogen runs out
A giant star is not simply a big star. It is one that has used up the hydrogen in its core and puffed up, becoming far larger and brighter than a normal star of the same colour. The very smallest stars never make the change, because they will outlast the present age of the universe.
The labels go back to Ejnar Hertzsprung, who around 1905 noticed that stars of the same cool colour could differ enormously in brightness, and called the bright ones giants and the faint ones dwarfs. On the modern diagram plotting brightness against temperature, giants sit above the main sequence where ordinary stars spend most of their lives. Confusingly, a hot, brilliant star still burning hydrogen in its core is properly a dwarf, however large. Giants can reach a few hundred times the Sun's radius.
What happens next depends on mass. In a star above about a quarter of the Sun's mass, the exhausted core contracts and heats until hydrogen starts fusing in a shell around it, and the outer layers swell and cool. A star below about 0.4 solar masses never gets hot enough inside to burn helium; it stays a red giant until the hydrogen runs out and ends as a helium white dwarf. Heavier stars reach about 100 million kelvin at the centre and begin fusing helium into carbon and oxygen.
Stars up to about 8 solar masses later burn helium in a shell around a dense carbon and oxygen core, which triggers a dramatic surge in size and brightness. Those from 8 to 12 solar masses can go on to burn carbon and even some neon. Above about 12 solar masses, stars are already so luminous that they only briefly pass through a blue giant stage before becoming supergiants; the hottest giants can outshine the Sun more than a hundred thousand times.
Below about a quarter of a solar mass, convection keeps a star's interior thoroughly stirred, so it can keep burning hydrogen for more than a trillion years without ever swelling. Mira, in the constellation Cetus, is a well-known red giant, and the prototype for a whole family of stars whose brightness rises and falls.
Source: Giant star
