Primary care is the provision of on-going care and usually includes screening (or referral for screening and interpretation of results), health education, and care of minor illnesses and on-going care for chronic conditions. Primary care providers should be able to handle common acute and chronic conditions. Patients whose disease does not respond to treatment prescribed by the primary care provider can be referred to a specialist or subspecialist.
So, someone may see a primary care provider who treats this person's hypertension, high cholesterol, type 2 diabetes, and mild arthritis (several of the most common chronic conditions in America). The primary care provider may also provide vaccines, annual "check-ups" and lab work, as well as treatment of acute illnesses and minor injuries. The primary care provider may refer the patient to a specialist if a problem does not respond to conservative therapy or if a very serious illness that requires a specialist (e.g. a patient comes in with a complaint of fatigue and bruising and blood work indicates an acute leukemia.)
Acute care means something treatment of something that has come on rather suddenly. I might get a sore throat, ear ache, and swollen glands. I need "acute care" but there is no reason for that care to be delivered in the emergency department. My primary care physician can take a look, order diagnostic tests, if indicated, and prescribe treatment (which might be limited to symptom relief for a virus or antibiotic therapy for a bacterial infection).
Preventive Medicine (as a residency) focuses on education/ advocacy/ administration /public policy and is closely allied with public health. Unless the person is doing a combined preventive medicine/internal medicine residency, those trained in preventive medicine don't provide patient care but focus more on research, health education, and the like.