While some consider a slave to be the same as a submissive, it can be more useful to consider a slave as being one who hands over authority to more than their involvement in BDSM activities to their master, as well as authority over how long they remain a slave. Thus, the slave's master then can command the slave in regards to how they dress, what they do in their spare time, and use the slave for service (such as cleaning, etc.).
The experience of surrender to their situation or condition as slave is more profound than for a submissive because getting out of it is not so easy. A submissive can simply withdraw their permission or consent at any time. A slave, on the other hand, is likely to have psychologically surrendered to not being able to reclaim authority, and that means that reclaiming authority is no longer a simple choice. It has become a difficult control issue with consequences for the slave's identity--i.e., if the slave knows that a slave can't release themselves and must be released by their master, then to somehow get to the psychological point where they can release themselves, they must also have broken or destroyed their identity as a slave.