They are both derived from the French world complaire, which means "pleased"
According to this source, "the two words overlapped in meaning until the middle of the 19th century."
How do they differ in meaning today, and why did they deviate? My understanding is that one refers to "not knowing" (something bad), while the other refers to "not wanting to know" it. Is this correct? Or are they still different spellings of the same word (which have been the case at one time?