Primary care is about long term coordination of medical care. In old school terms, think "GP" "general practitioner" "family doc," etc. The doc you see when you're sick and when you're healthy. The doc whose name you know. The doc who makes sure everything is working, and refers to a specialist when a complicated problem arises. Internal medicine, family medicine, pediatrics and sometimes OB/GYN and Psych count as primary care.
Emergency medicine is about someone walking into the ED, and then determining if they are sick or not. Sick ones need to be stabilized and handed off to an admitting physician. Everyone else gets sent home, and usually told to follow up with a primary care physician.
See the difference? They are, theoretically, complete opposites. However, with EMTALA and Medicaid, I can't say that's true.