In normal conversation, "illness", "disease" and "sickness" are interchanged a great deal. However, there is actually some specific difference, especially when used by physicians or any health organization.
An illness is a general term that people will use to describe themselves when they do not feel well. They may or may not have been diagnosed by a doctor.
A disease is more specific and is determined by a physician or health worker.
The term sickness is usually applied if people miss work or cannot function normally in society.
In general, "illness" is more general then "disease", which in turn is more general than "sickness".