While the same physician may call himself or herself all three of these titles, the titles do not necessarily overlap, and others would make a distinction. The short answer, then, is that they should not be considered identical and perfectly synonymous.
1) Your Primary Care Physician is the General Practitioner that your insurance company expects you to visit for general care. This doctor is usually specified beforehand and might be the only doctor covered by your plan except for emergencies/specialists (with referrals).
2) A Family Physician is a General Practitioner that sees both adults and children. (Unlike a pediatrician, for example.)
3) A General Practitioner is a general term for a Primary Care Doctor that isn’t a specialist. Insurance jargon has generally replaced this term with PCP in my experience. When you choose an in-network GP when you enroll in your insurance, that GP becomes your PCP.
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The term 'family doctor' belongs to a different era of single doctor practices.
Just to add that in the UK, on the NHS, we have to get a referral to a specialist such as a pediatrician. 'General Practice' is itself a speciality.