As a young military nurse in the British armed forces during the 1950's I was taught that contagious is disease spread by physical contact with the disease organism which could be as diverse as urine depopsited on food stuffs or untensils by a vector such as a rat a monitor lizard or any of a host more whilst infectious is disease spread by airborne means such as droplets expressed by coughing fo
I believe you are speaking about contagion and infection rather than contagious and infectious. The latter refer to how disease is passed from one individual to another.
The flu is a disease. The flu virus is its contagion. A contagion is the actual cause of whatever disease you happen to be spreading.
An infection is always a bacteria that has taken hold on some part of your body. For example, if your skin gets cut and bacteria start to grow there, you have an infection. It will be red (inflamed) and probably sore. If the infection goes untreted it c