I disagree with you. You’re making a false distinction.
If you have the virus, you are sick. You might not be sick enough to have visible symptoms. But the virus is replicating in your body. Your body is fighting it whether you notice it or not.
Nope.
You are sick when you show symptoms, Otherwise you are fine,
For example, I have plenty of viruses in my body from traveling and working in various third world countries in my lifetime, and I feel as healthy and strong as ever.
Most people with coronavirus don't even know they have it because they are feeling great, they develop anti bodies and just get on with their lives. No symptoms, no sickness.