flash is actually the type of memory device. it is a kind of Programmable read only memory. and is programmed on a page level ot a byte level. it retains its contents even if you turn of the power. some fancy physics, Fowler-Nordhein( FN) tunneling.
Bios is the basic input output operating system. basically the BIOS tells the mobo that it is a mobo, it has got so many bits and bobs and it's default values for this and that is this and that. SATA capability, USB capability ..
actually it would be nice if some one coudl list all the features in the BIOS