I've been reading a lot of professional blogs about GFCI protection and was a little disturbed so much was either confusing or wrong, so let me clarify what exactly a GFCI protection (outlet or breaker) does.
Much like the astrological sign Libra, GFCI's are constantly looking for balance. But balance where you may ask? The balance in this case is between the current flowing through the hot wire and the neutral. In a well functioning outlet the current flowing from one is the same as the current flowing into the other. So long as this balance is maintained the tiny coils inside maintain equivalent pressure and the outlet or breaker continues to work.
Now lets take an example of a person with wet hands who inadvertently comes into contact with a live conductor. Current then flows from hot, through the person to a ground path such as a sink or the ground and flows back to the electrical panel. The circuit is completed by the human being instead of by the neutral wire. This causes an imbalance in the current flowing out of the hot, because part of the current is now flowing through the person and never returns to neutral. Because it takes very little current to stop a heart (~ 10 mA) only a tiny bit of imbalance is needed to trip. For instance, Class A GFCI units trip at around 5mA.
Incidentally, 5 milliamps is 3,000 times less than the current needed to trip a common breaker, at 15 Amps. So you can see why a breaker isn't up to the task of shock protection.
What about 2-pole GFCI breakers?
With the 2023 National Electric Code (NEC) many homeowners are starting to see GFCI breakers for the dryer and electric range when present. The same principle applies but it's a little more complicated. With 2 pole devices there's 2 hots and a neutral. Depending on the feature current may flow in a range of combinations. For instance, control circuits and lights are 120V but the heating element is 220V.
The 220V circuits would flow from one hot to the other (black to red) but the 120V circuits would flow from one hot (black) to the neutral (white). So long as the GFCI breaker "sees" all of the current in and coming out all is good. As soon as there's an accounting error however they will trip.
The need to account for 100% of the current flow is why GFCI breakers always require the neutral to be plugged into the breaker as opposed to directly to the neutral bar.
Breaker vs. Outlet
A breaker with GFCI features and outlet with GFCI serve the same function and may be used interchangeably. The difference is convenience, cost and size. For instance the NEC now requires clothes washers to be GFCI protected. In my case, I can't really get to the outlet. It's behind a stacked washer and dryer and resetting the outlet would require movers. Instead I use a GFCI breaker. Should the outlet trip I can reset it from the panel. The same is true for my microwave and disposal. I could use either option but the breaker is much more convenient.
The outlet is cheaper but larger and bulkier. The kitchen counter, bathrooms and outside outlets are all easily accessible so best served by an outlet but the NEC does not mandate one solution or the other. Technically I could put in nothing but GFCI breakers and the code requirements would be satisfied.
Surge Protection
Most GFCI outlets do not incorporate much surge protection at all. A basic MOV to protect the delicate GFCI circuits is included but you really should not think of these outlets as surge protection devices. Same for the breakers.
Some writers online have used the term "ground surge" to describe what causes a GFCI device to trip and this causes many readers to assume this makes a GFCI outlet a surge protector. I wouldn't call 5 mA of current a surge, but in any event no, a GFCI outlet is not also a surge protected outlet.