Suffering is the experience of that. We've all had times when the same level of external stimulation may be perceived as much more painful than at other times. So we can't always control pain, but our experience of pain is something that is often affected by the amount of support that we have. The same is true for disease and illness. Disease is the physiological process.
Illness is the experience of that.
With illness, while no one searches for that or wants it, there can often be a transformative quality about it. We don't look for suffering, but it's there. How we deal with it is something that we have much more control over than we might realize. The same is true for healing and curing. Curing is the physiological process of getting better.