I'm assuming that you're talking about these words as verbs, in the context of a disease. Otherwise, they both have other, unrelated meanings, such as to treat someone to dinner or to cure meat.
To cure a disease is to remove it from the body so that the patient no longer suffers from it.
To treat the disease is to reduce the suffering and keep the disease from getting worse, or at least to manage it. Treatment may eventually lead to a cure, but it may not.