Is a GFCI receptacle device a circuit breaker?
No.
Each type of device serves a distinctly separate protective purpose.
Breaker
A circuit breaker detects overcurrent faults, it does not detect ground faults. A circuit breaker will stop your house catching fire when the wiring in the walls overheats from prolonged overcurrent, it wont stop you and your family being killed by electrocution.
A typical UK breaker protecting a 6A circuit might only trip out when the current reaches 30A. There are several ratings in the UK:

Type B trips between 3 and 5 time full load current;
Type C trips between 5 and 10 times full load current; and
Type D trips between 10 and 20 times full load current.

The reason for this is that some appliances have a high inrush current and you don't want lots of nuisance trips.
It is probably worth noting that breakers don't trip at a specific current, it depends on how long that current is sustained. A small overcurrent will take a long tome to heat wall wiring to dangerous levels, the breakers typically take that into account.
GFCI
A GFCI detects ground faults, it does not detect overcurrent faults. This is mostly designed to prevent electrocution. It won't stop your house catching fire.
The assumption here is if the current supplied on hot is more than is returning through neutral, the difference might be flowing to earth through someone's body.
A class-A GFCI may trip out for a very low imbalance in current between hot and neutral, perhaps only 5 mA (i.e. five thousandths of an amp).
The UK equivalent, an RCD, might trip at 30 mA - there are many types designed for various purposes - which is why it is sometimes best to employ a professional electrician to select and install these.
AFCI
An Arc Fault Circuit Interrupter (AFCI) is designed to detect arcing. This is where a poor connection, for example in a plug or outlet, causes sparking as the electric current crosses a small air gap. These are the types of faults that can cause fires even though the current being drawn may be well below what will trip the breaker.
Combination devices
UK
In the UK you can use an RCBO that combines RCD (GFCI) and MCB (circuit breaker) functions in a single device in the &quot;consumer unit&quot; (main distribution panel).
A typical UK installation would have two RCDs in the main distribution panel. You can buy plug-in RCD devices. You can buy sockets with built in RCD protection - mainly for outdoor use where an electric mower might cut it's own lead.
US
The US have similar combination devices. They can combine breaker and GFCI or all three functions.
From what I've read, historically, there seems to have been a practice in the US of putting breakers in the panel and GFCI in the outlets. One GFCI in a circuit can be used to protect ordinary outlets downstream of it. Nowadays people tend to use GFCI, AFCI and combination protective devices more.
Regulations
Nowadays you generally need all types of protection.
Usually, existing installations don't need to be brought up to date unless you are making significant changes like adding new circuits.
Obviously, regulations vary from place to place. You need to check what applies in your location.