Maybe it's just semantics to me, but the defining factor to me has always been how much free will is given away (willingly or unwillingly). If an individual still has choice he or she is a submissive. If an individual has had choice stripped away unwillingly, or given away willingly, he or she is a slave.
This is more similar to what I was taught by My Dom Mentor.
A submissive always has a voice, choice and ability to say no. they have decided to give up power willingly to a Dom/Domme that they choose and have discussed terms and limits with. A submissive would have total control over whether they want to end a relationship with a Dom/Domme, even without reason, though a well-trained sub who first chose that Dom/Domme, would not do that and would communicate why they're ending the relationship, hopefully after using communication to try to fix the issues.
A slave is one who loses or gives up her voice, choice and ability to say no. Some might give that power willingly and totally unto a Dom/Domme, knowing they'll be molded into what their Master/Mistress desires, the longer of which they stay and are molded, have a harder time breaking away if something changes. When done unwillingly, they are usually broken faster and more completely with more restrictive Masters/Mistresses, and find themselves unable to escape, without some sort of outside help from another sub, slave or Dom/Domme.
A Dom/Domme is simply a person with a Dominant personality, and doesn't necessarily mean they will take on a sub just because. It's done when They feel something missing and those trained, are usually careful in selecting a sub and actually hope that the sub is doing the same, as the commitment, time, care and affection involved in that relationship brings a lot of T/themselves into it. A Master/Mistress is someone with a sub and in that position of care and responsibility over another person, taking the gift of their control seriously.
Just like there is subcategories in, let's say, breast play on the O/O Matrix here...pinching, biting, branding, piercing, binding, clamps (don't remember what's actually under it, but hopefully you get the idea), and you can select what you like and don't like about breast play or pick breast play in generalization, is the same as what a slave means to any one or other person. Like, what a sub does with his/her Master/Mistress might be different than what their sub friend does with their Master/Mistress. Nothing is ever the same with any two people and just reinforces why communication is so important at the beginning of the relationship and throughout as each and both grow within it.