I think you mean "conscience".
"conscience" relates to ethics and morals, whereas
"consciousness" relates to theory of mind and self-awareness;
the latter term pertains more directly to the theories of cognitive neuroscience under discussion here.
Sorry I didn't specify the root of both words are homophones, I figured that would be obvious from context.
Turns out it can mean two words sounding the same (definition 2) or merely sounding alike (definition 1). Personally I always thought homophones had to sound identical. But you are right, they are homophones in the broad sense.
I think they have the same root [1].
[0] https://www.merriam-webster.com/dictionary/homophone
[1] https://www.merriam-webster.com/words-at-play/usage-of-consc...