To add a bit of context:
They're interchangeble terms at times. But I see a couple of basic distinctions in how they're generally used:
- Disease is the more clinical term.
- Illness doesn't convey as much severity of the condition.
For example,
You could say, "Dr. García treats diseases of the nose, throat..."
You could say, "Mary was out of school for a couple of days due to illness."
You would not say, "Lung cancer is an illness characterized by..."
Perhaps in Spanish there's no need to distinguish them if "enfermedad" covers a broader range of meanings than the English words do?
Hope this helps.
Saludos.
Vicki