i have a slightly different point of view that is a bit less technical, not going by the definition of either word, but what is felt, at least in my heart.
currently i am neither sub nor slave, i am unowned, uncollared, though the submissive side in me is very strong. i believe that one can simultaneously be a submissive and a slave. Allow me to expound.
Let's pretend i do have a Master, and in every day intereaction, i am His submissive or slave if You will, whichever you prefer, longing to nay displease Him by following His every command. Should i fail, he understands the err's of being human and perhaps may still discipline me. In that sense, i am a submissive, striving, but still having limits. However, away from Him, when He is not there, my every jesture, my every thought, my every action and movement displays all the beautiful things that would make Him proud to call me His. I do these things, even though He cannot see me, because He has trained me and molded me to His will, and because my belly burns to be more beautiful and pleasing to Him everyday. In this sense, i am His slave. i believe when One truly owns Your heart, it is inevitable, you are a slave to that person, whether either of You wish it to be or not.
That is just my opinion on the subject however, for whatever it's worth. Like i have said, i am completely new to this and have never been owned, but i believe i have a bit of understanding of the beauty of a D/s relationship. Any advice or input would truly be welcomed, as i may be completely off base here.