Could daily exposure to rust cause tetanus or some other type of illness?

Not tetanus. Tetanus is caused by bacteria that may live on rusty nails and is introduced by a puncture wound. Chronic exposure to rust dust can lead to inhalation and abnormal chest xray findings as well as exacerbate airway reactivity.
Confusing Xrays. Rust in and by itself does not cause tetanus. However, chronic exposure to a cloud of rust particles could cause confusing chest xrays. Particle filters & masks are recommender in occupations where this is expected. Small rust particles can be inhaled into the deep areas of the lung & settle in. Xrays look sickly but patients tend to be asymptomatic. (siderosis).