A red giant is a substantial and luminous star in its final stages of life, while a white dwarf is a small, dense remnant that has depleted its nuclear fuel.

Red giants form when a star exhausts its hydrogen fuel in the core and begins the process of fusing helium. This transition causes the outer layers of the star to expand and cool, resulting in a red appearance and significantly increased size. Red giants can be up to $100$ times larger than their original size and can exist for millions of years before ultimately shedding their outer layers and evolving into a white dwarf. The luminosity of red giants, which increases as they expand and cool, is a crucial characteristic of this phase in the stellar lifecycle, as discussed in detail on the relevant page.

On the other hand, white dwarfs are the remnants of stars that have completely depleted their nuclear fuel and collapsed under their own gravity. These objects are remarkably dense, possessing a mass comparable to that of the Sun but a volume similar to that of Earth. White dwarfs can reach temperatures of up to $100,000$ Kelvin, yet they no longer generate energy through nuclear fusion as they did during their earlier stellar life. Instead, they gradually cool over billions of years, eventually becoming cold, dark remnants known as black dwarfs. The electromagnetic radiation emitted by white dwarfs can be further explored for a deeper understanding.

In summary, red giants and white dwarfs represent two distinct stages in the life cycle of a star. Red giants are large and luminous in their final phases, while white dwarfs are small, dense remnants that have exhausted their nuclear fuel and are slowly cooling over an extensive timescale. The transformation from red giants to white dwarfs involves intricate nuclear processes, predominantly centered around the fusion of helium, as outlined on the designated page.