How, then, does consensual slavery differ from submission? Is no another way to see this.
First and foremost, slavery hinges upon a commitment to obedience. The slave does not revisit issues such as "should I submit?" or "How do I feel about that? Will I say yes or no?" When a dominant order is issued, whether or not the slave agrees with it, sie is obedient in the same manner that a soldier is who has enlisted in the Army. (That military analogy is one of several I think holds very true for the power dynamics of M/s relationships.)
Secondly, in consensual slavery a person gives themselves over to the control of another as completely as is humanly possible. This means not only a high degree of obedience, but that there is actually a chattel property context to the relationship. I refer not to a legal relationship, of course, but to a mutual understanding of ownership and property status that arises between the parties. While both slaves and submissives are often fondly referred to as "property", in the sense of consensual slavery the slave becomes literally (by mutual agreement) the property of the Owner. It is not unheard of for slaves to be sold by an Owner and to go willingly to their new Master or Mistress.