An infection case is one affected individual counted in an outbreak model. A count of eventual cases can include exposures that have occurred but whose delayed transfer into the infective compartment is still pending.
An infection involves invasion and multiplication of an infectious agent in a host. Bacteria are one possible cause; an agent capable of causing disease is a pathogen. The National Cancer Institute defines infection through invasion and growth in the body. [ref].
In a SIR model, acquiring infection moves a member of the susceptible compartment into the infectious compartment. That immediate transition is a model assumption: the SEIR model instead includes an exposed stage before infectiousness. Specify these states when translating a biological process into compartmental models.