In common D/s relationships the sub only submits occasionally and with definite short-term goals, perhaps for an evening or the duration of a party.
In longer, committed relationships many people opt for the Master/slave model, in which consent is negotiated once for a long period and the consent given is generally broader. Some people opt to be purely "sex slaves", while others who prefer domestic service identify as "service slaves". Some slaves allow their Masters or Mistresses complete latitude as to the demands that can be placed on them. Such a relationship is known as "Total Power Exchange" or TPE), where the slave has given all control to the dominant partner, whether with or without a contract. Whereas in the Dominant/submissive relationship, the submissive tends to have more 'rights', and be able to use their safeword to stop a scene, a slave may not have that luxury.
A Master/slave TPE relationship can be one of the most difficult relationships in the BDSM world to maintain, and requires special skills and experience, on both the Master's and slave's parts.
Some people opt to be purely "sex slaves", where their sole duty is to please and pleasure their Master. Others who prefer domestic service identify as "service slaves". As usual, there is much blending of the two, as well as other classifications of slave.