In NOR Flash, if you overwrite data, the result is the AND (or the OR) of the old data and the new data; that is, you can write 0 bits, but not 1 bits. Erasing is a separate and much, much slower process, which is why it's done a sector at a time instead of a bit at a time.

In NAND flash, overwriting isn't even an option, although I don't understand why.