In the textbook's limmī illustration, corrupted humors are hypothesized as both a real cause of fever and the middle term through which fever is inferred. In the innī illustration, fever indicates the supposed humoral condition without producing it.
A concise distinction is:
Limmī: the argument answers “Why does it occur?” by identifying the cause.
Innī: the argument answers “How do we know it?” through evidence, potentially an effect of the cause.
Neither classification can be justified by word choice alone. The actual relation between middle term and concluded predicate must be examined.