Things vary by program a lot. I have personally done each of these things mentioned: two months on gyn/urology as a pgy3, doing hysterectomies, c-sections, laparoscopy; I did my vascular as a pgy 2 with a cardiovascular-thoracic group where you could scrub all the cardiac cases you wanted; as an intern we did a month of neurosurgery where one of the surgeons would let the resident "do a case" at some point in the month-open, resect tumor, and close-with a lot of help of course; on trauma it isn't all that uncommon to work up seizures, guy passes out and crashes car, you have to work up why, and many trauma services use consultants sparingly, doing workups themselves.
General surgery education is geared towards training you to be a whole body surgeon, though now the practice once you graduate is general surgery. When you take your boards you will be expected to know vast amounts of vascular, thoracic, trauma, pediatric surgery, ENT, gynecology, etc. This is a field where the training is 5-7 years. Also, it is not really a field for those who haven't selected a track, as mentioned above, like vascular, thoracic or plastics, because those really aren't the way that things work at most places (though more so with plastics.) General surgery is for people who aren't sure necessarily whch of the fields they want to enter other than not ortho, not urology, not ob, not ENT. Also as a surgeon you are expected in practice to know it all: you may be on call to an er and have to do a traumatic anything: thoracotomy, cardiac surgery, c-section.
I haven't seen more than a few seconds of the show. I bet though that the training is more and less exciting than on tv. It is an exciting field: you make life or death decisions very commonly, and encounter situations where its go time all at once. But not too glamorous: personal hygiene reaches new lows, lives have little else in them but work and family, you are chronically sleep deprived, and have 5 things that you should have gotten done last week, e.g. medical records, research projects, studying for textbook rounds/absite/boards.
All that being said its fun, exciting, stressful and fulfilling.
Just my 2 cents.