Does the plague effect children, the elderly and adults differently?

In treatment only. The main source of infection for Yersinia pestis, the cause of bubonic plague, is by contact with rodents and their fleas. Therefore, children may be more likely to handle rodents or other animals in certain circumstances. Otherwise, the elderly may have a poorer prognosis as in most other illnesses. Tetracyclin, a common treatment, is not suitable for children under 8 years.
See below. The extremes of age (children and elderly) and those who are immunocompromized are going to be more susceptible.