One can get into some interesting semantic discussions about "what is sub vs. masochist vs. slave".
As a Dominant (and Master when I have a counterpart, as I do now) here are a few helpful suggestions:
Submissive: Someone who wants others to control situations and stimulation for both their own feelings AND to see the happy reactions of those they are serving. The feelings and sensations that the submissive feels are important, but the reaction of the partner is more important to them. This does not always need to be sexual in nature (but often is). "Service Subs", Vallets, Dolls, Pets, Maids, etc can all be roles for a submissive and some serve in different capacities at different times.
Masochist: Someone who wants pain (physical/emotional/situational) inflicted upon them by another person so that they can feel and get in touch with their inner-selves. The reaction of the partner can be important, but is secondary to the stimulation for themselves.
Slave: Someone who has given up responsibility for their safety and volition to another person or persons. They have given up safety nets such as "safe words" and allow their Master/Mistress to determine their lifestyle, physical sensations (including orgasm), sexual partners, and tasks.
Sadist: Someone who enjoys inflicting pain or other intense sensation (Physical/mental/situational) upon another. The other person's reactions are important, but secondary to the Sadist's enjoyment of the scene.
Dominant: Someone who enjoys exercising Power over another person. This can be sexual or non-sexual forms of service, and while a major factor is the Dominant being pleased, the reactions of their partner are also part of the Power and stimulation the Dom/Domme feels.
Top/Bottom: Similar to the Sadist/Masochist, but without the Power and control implications, more for sensation. For example: a Dom might order their sub to flog them because they like the sensation. During that scene the submissive may be "Topping", and the Dom "Bottoming", but the order and power structure still remain intact.
Human beings are complex. Our sexual/romantic lives may be the most complex aspect of ourselves...and people CHANGE over their lifetimes, so don't regard any of these as a hard and fast "rule", most people are a mix at various times and with various partners or situations.
For myself, I've been a Dominant for over 40 years and Power Exchange is pretty much fused into my emotional ability to love and be intimate.