to be honest I think that it really depends upon the Dom and sub. For every couple those terms could mean something different. I tend to believe very closely as you do. But some may take a lighter meaning to the word slave...or even for it to mean the same thing as a sub.
I think really the only way to discover what it means is to have it applied towards you and find out how it makes you feel, what the implications are, how its effects you and your Dom.
I like the term submissive better than slave, however there are times I enjoy being called a slave. As a submissive, there are many ways in which you are a slave to your Master. Does this have to be negative? No, not at all. People can be slaves to.... music... hobbies... food.. etc. Why not a person? Its does not have to suggest an unwanted servitude, only if thats what you and your Dom decide thats what it means for you.
As far as being collared vs. uncollared... nothing -really- changes.... many things stay the same. BUT.. things like trust, bonds, love, can grow. Often times this is when a D/s choose to focus on one another and no longer play with others (unless it is an open relationship)..... more terms may be agreed upon, more training, greater tasks and expectations. BUT with all of that comes much more loyalty, trust, love, etc... you become closer.
Its similiar to the change of dating to marriage. Nothing realllllly changes, the changes are small, but signifigant, meaningful..
Thats what it all means to me anyway.
I would suggest you find out what being a sub and a slave truely mean to you.. without the stereotypes that accompany them, because all things in this lifestyle can be tailored to fit you and your needs with the help of a crafty Dom.
So don't settle on one thing.. describe what you want and need and go from there.. then you will find your place.
I hope that helps.. :/
anya