Nurses do the minute by minute care of the patient, they're mostly the ones the patients call if there's immediate issues whereas doctors are responsible for overseeing the care of a patient, diagnosing diseases and writing care plans.
Depends on the type of nursing your talking about, big difference between Enrolled Nurse, Registered Nurse, and Nurse Practitioner. NPs do what you mentioned for doctors. The role of the EN and RN, is a focus on patient care, assisting with activities of daily care, observation of patients, administration of medications etc, doctor and NP is focused on the medical aspects of the patient, diagnosis, prescribing, pathology etc.