In your home there are three basic types of circuit breakers for three specific types of purpose. The thermo magnetic trip breaker, the GFCI breaker and the ARC Fault Breaker.
Thermo Magnetic trip breakers have been around for almost 100 years. They are designed to measure the current inrush through either magnetism or heat. The are the most common type of circuit breaker used and are sized to protect the wire in your home. The have no other purpose other than to protect wire, the are not designed to protect items plugged into your wiring or even devices connected to the wire.
Arc Fault breakers were invented about 20 years ago and have just recently become mainstream. The are designed to protect everything in the circuit from fire, including the lamp you plugged in. Often when an item shorts out, it does not create enough energy to trip either the magnetic or thermo device in a common breaker, thus ARC faults were created to monitor the circuit for small occurances and turn power off to that circuit.
GFCI breakers were invented almost 40 years ago. They are strictly intended to protect life. The monitor the electricity to ensure power is being used correctly and not "leaking" back to ground. These breakers work exactly the same way as GFCI receptacles work.
Both GFCI and ARC fault breakers are designed as thermal magnetic trip breakers as well so in addition to the added protection of either ARC fault or GFCI, they also work as a traditional breaker protecting the wire as well.