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A White Dwarf has ceased fusion. It is effectively dead. As it cools it shrinks (which means it emits more energy per unit surface area and shows as white.
This is the remanant core of a larger star that has shed a planetary nebula, stopped fusion and does not (yet) collapse due to electron degeneracy pressure.
Some simply continue cooling indefinitely and fade, some in a binary may acquire more mass and produce a type 1a Nova.
There has not been enough time for any white dwarf to form and cool to a temperature that does not emit light.
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Over a very long period of time a white dwarf eventually cools to form a red dwarf before finally fading into invisibility. There are a lot of red dwarfs out there because the cooling process takes as I said a very long time.
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Eventually it turns into a black dwarf, it ceases to emit light or energy. There are no black dwarfs at the moment as the Universe is not old enough for that to occur. We do have a very dull white dwarf on record and it is estimated to be 12 billion years old.
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It just slowly cools off, so that after trillions of years it would just be a cold body like a planet. That stage is sometimes called a black dwarf, but the universe is not old enough for any to have cooled that much yet.
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It gets dimmer and redder and cooler until it fades out. This has never yet happened though. The universe isn't old enough for there to be any black dwarfs in it.
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As it cools it radiates less heat and light. Once no more heat or light radiates the star becomes a black dwarf.
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Becomes neutron star & further a BH.