If I cough and leave the room and you come in and breath the droplet nuclei suspended in the air, that's indirect transmission and air is the intermediate. Food is a good intermediate. Fomites are inanimate objects that carry infectious microbes. If I cough and the microbes fall on the desk and the next person who sits there picks them up on her fingers and then bites her nails, the intermediate is an inanimate object the desk, a fomite. Kleenex, door knobs, toilet seats, faucet handles.
Vectors are animate insect intermediates.
Mechanical vectors are insects like flies that carry pathogens outside their body. Biological vectors are intermediates that carry pathogens inside insect body as active part of their life cycle. Carriers are humans who have infectious pathogens colonizing their bodies. Human vehicles do not carry the microbe in their body, but only on their body. Dorms,day care, schools, but the most common is transmission site are public toilets.