As a point of personal opinion, I'd like to define the differences between very basic terms so that there is no confusion as to who I am referring to when I mention either of these terms. I write this guide in my perspective and provide my mentorship and guidance with these terms clearly defined for me. I welcome varying viewpoints in the comments so please feel free to disagree civilly and provide your own view.
There are several other names that can be 'classed' for the submissive role in a relationship. The ones I'm covering here are the basics. I am well aware of toys, pets, sluts, servants and many many other names. Please do not feel that I am not leaving you out, but for the sake of clarity and simplicity, I am covering only Bottom, Masochist, Submissive and Slave.
A bottom is the lower role within a play session. Generally, the person does not submit outside of the agreed upon time that both parties are enjoying the physical aspects of play. Bottoms have more control over what happens in the scene than other submissive types.
A masochist is someone who likes to receive pain for pleasure. They can be the bottom in a scene but the reason I gave it a separate designation is that there are Dominant roles that are also masochist.
A submissive is someone that submits in a relationship either part of full-time. This can involve only in the bedroom play all the way to live-in service. A submissive generally submits only to those they are in a D/s relationship with and are respectful of others outside of it. A submissive has roles and rules and structure to guide their interactions with their Dominant and with others. Most of the time they still hold a veto card called the safeword.
A slave is a separate form of submissive. They hold no limits other than what their Masters give them. They can not refuse service to their Dominant. The argument has been going on since the beginning of time about the real differences and so I'd like to set up right here what I believe so that you can understand where I am coming from when discussions happen on this site. A slave is on a deeper more intense level of service than any submissive could work up to. If someone says they were submissive and became a slave, it is because they were always a slave and are now finally identifying as that. Becoming a slave is re-identifying yourself, not just a progression but an intensification of submission.
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Feel free to share your thoughts in the comments! What name to do you rest well under?