Answering my own question.
Both are "sickle cell diseases", but they are specific forms of a sickle cell disease.
"Sickle-cell anemia" is the name of a specific form of sickle-cell disease in which there is homozygosity for the mutation that causes Hgb S. Other forms of sickle-cell disease include:
sickle-haemoglobin C disease
Unlike sickle-cell anemia, these other forms of sickle-cell disease are compound heterozygous states in which the person has only one copy of the mutation that causes Hgb S and one copy of another abnormal haemoglobin gene. It is important to know that "sickle-cell anemia" is the proper name of a specific type of "sickle-cell disease", and that "sickle-cell disease" is a non-specific term. Because the different forms of sickle-cell disease are quite different, one must be sure to specify the exact form of the disease in question.