In the US, the medical industry has become all about specialities in the past 20 years. Plastic surgeons earn more money than pediatricians, who earn more than general practitioners. Any person who has earned a medical degree and has completed the necessary on-the-job training (
residency) and has been appropriately licensed in the US is called a "physician." Personally, because I suffer from
Lupus, my primary care doctor is my
rheumatologist. However, he is also an
internist, so luckily he is able to diagnose and treat my non-Lupus complaints.
Anyone with the proper degree(s) and credentials is called doctor, but a
podiatrist wouldn't be the proper physician to diagnose and treat your diabetes or lung cancer. That's why it's very common for physicians to refer to themselves by their specialty; instead of simply saying "I'm a doctor" they'd specify "I'm an oncologist" or "I'm an orthopedist."
In the US, every surgeon is a doctor, but not every doctor is a surgeon. A
surgeon has had specialized training and actually cuts into the human body and performs invasive procedures.