Two separate points
If you are contagious then every time you cough, lock your finger, wipe your eye the virus will go onto your fingers, onto whatever is around you. You will leave a trail of virus wherever you go unless you are fastidious. Anyone else touching the button, handle, packet of pasta which you touched or coughed on will get the virus
If you are NOT contagious then every virus coated button etc you touch, you will pick up some virus and potentially spread it to the next button you touch, therefore someone not immune migjt catch it from you spreading
Given the virus doesn't stay live for days and days, it's quite easy to see that both people can spread it, but infected people spread it much more
Non infected people will only increase the spread of what is already out there.
Infected, contagious people will add to what is out there
The two are very different things