The main difference between a submissive and a bottom is that the submissive does not give instructions, although they do set limits on what the dominant can do. A bottom is not necessarily a submissive; they may enjoy intense physical and psychological stimulation but not submit to the person delivering it. Similarly, a submissive might not be a bottom; they may enjoy taking orders from a dominant without receiving any physical stimulation. For bottoms who are not submissive, the bottom is most often the partner who is giving instructions—the top typically tops when, and in the manner, requested by the bottom.
A slave is a submissive who consensually gives up total control of one or more aspects of their life to another person (sometimes called their Mistress or Master). The slave will often accept a collar from the person to show that they are owned.