Hello Serenitypup~
For me the easiest explanation is to say a Submissive submits to their Dom/me in ways that are pleasing to themselves as well as the Dom/me primarily. Submissives may have and retain Choice and Limits. ie Choose what they will Submit to. A Slave Submits to their Owner, and it is the Owners pleasure the Slave seeks to be, even when what is pleasing to the Owner is not pleasing to the Slave. The pleasure for the Slave is in pleasing their Owner.
A Bottom is not necessarily a Submissive, and is surely not a Slave.
Overall as Delia suggests reading the Topic she has presented, you may find more of what you seek there in answers.
Respectfully~SidheWolf