A white dwarf is a white hot solid ball of nickel-iron alloy, a black hole is an infinitesimal singularity of infinite density surrounded by total emptiness.
their colour is one thing but a black dwarf originates from a white dwarf
A white dwarf will cool very slowly to become a black dwarf. This process will take longer than the current age of the universe.
size and color
There is a great difference in temperature between black and white. Black clothing tends to absorb heat more than white.
A white dwarf star is created after a nebula and the black dwarf star is created after a nova
A black dwarf.
No in the life cycle of a star, a white dwarf can cool and become a black dwarf
A black dwarf is a dead white dwarf. By dead, I mean a star that no longer burns. A white dwarf, in turn, is a dead "moderate" star (a star like our sun). So a black dwarf is a star that's died twice, with mass not much higher or probably lower than that of our sun. A supernova, is the "death" of a star that's really huge. By huge, I mean it has a mass that's considerably higher than that of our sun. That kind of star doesn't turn into a white dwarf. Rather, it becomes either a neutron star (pulsar or non-pulsar) or a black hole.
Red giant - Black dwarf. See related questions.
Black Dwarf.
a black dwarf
A cooled white dwarf is a black dwarf. I think you are thinking of a neutron star which has nothing to do with a white dwarf.