I've understood that a virus is not a living organism (like e.g. a bacterium). From Wikipedia I get that a poison is a substance that reacts physically or chemically with molecules in the human body. Since a virus is a protein that binds to certain cells in the body and alters the cell's function in a harmful way (resulting in the production of more viral matter), why is a virus not a type of poison? (Or is it?)
Additional info: I'd like to understand the difference between them—if any—on a chemical and physical level, as well as the consequences for treatment. For example: we all know by now that viruses can only remain harmful/intact on surfaces for a certain amount of time. However, I would think that a poison on a surface does not have such a time limit (but I may very well be wrong). What's the difference, if there is one? Why is licking a banister with viral load older than 4 (or so) days not harmful, but is licking a banister with poison older than 4 days?