Generally speaking (no pun intended), and in the urban context at least, a GP is a primary care doctor, your "family doctor" kind of role, working in the community (i.e. in a GP clinic and the like). GPs are generally the first point of contact for patients (unless they went straight to the Emergency Department).
A physician, on the other hand, would generally be a hospital doctor specialising in a medical (as opposed to surgical) specialty. So we're talking about the likes of cardiologists, respiratory physicians, gastroenterologist, nephrologists, endocrinologists, neurologists, paediatricians, geriatricians, haematologists*, infectious diseases specialists*, rheumatologists, medical oncologists, etc. (*: some require dual training, e.g. haematologists and infectious diseases often have dual training between physician college and pathology college.)
A General Medicine physician is a physician who has training in General & Acute Care Medicine; and Gen Med (in my limited experience and understanding as a former med student) tends to handle acute medical^ hospitalisations that don't go straight to a particular medical^ specialty; undifferentiated presentations (cases that are hard to figure out); or cases requiring input from multiple specialties. This is as opposed to "heart attacks" (acute MI) going straight to cardiology, or strokes going to neurology or dedicated stroke unit. Notably, at least in NZ, many physicians dual-train between Gen Med and another medical^ specialty - e.g. GM+cardio, GM+resp, GM+neuro, GM+endocrine, GM+InfectiousDiseases, GM+ClinPharm, etc.
(^: "medical" meaning internal medicine, as opposed to surgical / obgyn / psych.)
A GP never really knows what the next patient will come in with, and need to know "a bit of everything" - medicine, surgery, Obs & Gynae, psych, paeds, dermatology, etc; they need to do screening (cardiovascular risk, blood pressure, prostate exams etc etc), they need to be good at managing things that don't need a hospital specialist (most commonly hypertension, diabetes, asthma, etc), know and recognize red flags for serious concern (symptoms and signs indicative of malignancy), and know when to refer patients to specialists, which specialty to refer to, and how urgently - should you send the patient straight to ED by ambulance, should you phone the hospital and send patient there in a couple of hours with a letter, or is it just a matter of posting a referral letter for a potential outpatient consult in a few months? Some GPs perform minor surgery too (skin lesion excision etc).
