no, I know many submissives who have no say over anything in their lives - when they eat, drink, pee, talk. Some people just totally reject the word slave because of it's historical background and some just don't use it to describe themselves. That's why talking about relationships with a power exchange, and whether that power exchange is total or partial covers all kink based relationships with an unequal dynamic, rather than trying to use a prescriptive label to make distinctions between relationships that vary so greatly.
Everyone has an out, everyone uses it if they are in an unhealthy situation which makes them unhappy. The only ones who stay are the ones who would stay in a vanilla relationship that made them unhappy and that has nothing to do with "Da Rulez", it's simply because they think they don't deserve/can't get anything better ie low self esteem or they get into that mondset that love/marriage/whatever means that you absolutely must strive through misery to prove your commitment and love to one another. Trying to differentiate slave and sub by saying a slave is the one who gives up all their say regardless of their personal feelings just isn't apt. Saying a sub is the one who can just rescind their agreement at will isn't apt either:if you are in any type of power exchange, saying "no" will always affect the dynamic negatively. It isn't just going to pass without notice simply because you identify as a D Type's submissive rather than their slave. It could potentially ruin your whole relationship. It makes absolutely no difference whether you are a slave or a submissive, it completely depends on the nature of your D Type and the specific rules of your individual relationship.
This actually matters when it comes to polyamory because when you identify as an s type of some sort, people assume that if you are already in a relationship it will be a certain way because that type of s type has relationships with these sorts of rules. My Daddy, for example, isn't ultra protective, doesn't want to vet everyone I meet and thinks I should fuck more men. He is turned on by me getting fucked by other people. Someone the other day on Fetlife (after seeing we have our profiles linked Daddy and babygirl) said that they didn't contact me because they thought that it meant he would want total control over everything and that I am only allowed to date females (despite being straight) because from his experience, babygirl's are only usually looking for sister subs that they have sexual relationships with and secretly hate. The chances of me referring to a metamour as a "sister" is slim to none.
Lastly, openly disagreeing with me about something in a way that suggests that I am wrong and then suggesting that we leave the conversation there just isn't going to happen. Sorry.