Well, team nursing has taken on a bit of a different definition since I graduated 30 years ago. Basically, it means that you have a team of nursing personnel that divvy up the tasks and patient care that need to be done among them. Nowadays that has evolved into splitting up the team leaders assigned patients among herself/himself and any LPNs or CNAs on their team. The licensed nurses usually give the medications and IVs to their patients. The RN assumes overall responsiblity for making sure that all the care gets done for the patients on her team. This makes you a kind of manager. There are some tasks that only an RN can perform so to account for this use of her time, the team leader often takes a lighter assignment. In my day, we split our teams differently. We put a nurse on meds for all the patients in the team. Our CNAs, if we had them, were assigned easier patients to do basic nursing care on while the LPNs were given the bed patients and those patients who needed dressing changes or other treatments that they could do. The team leader made rounds with the doctors, called the doctors for orders and signed off orders from the charts and made sure the new orders were communicated to the other members of her team. Some places call this person a charge nurse.
Primary care is where you, the RN, are assigned a group of patients, perhaps 4 to 8 and are expected to do everything for them: meds, IVs, baths, turning, ambulating--everything.