A GFCI breaker compares the current in the 'hot' and 'neutral' legs of a circuit, tripping when they are different by a miniscule amount (i.e. the current is 'leaking' to somewhere it shouldn't, like through your body).
An Arc Fault breaker detects when, though the current may be staying in the desired current path, there is a bad connection that is causing arcing and sparking which in turn creates heat build-up, a major contributer to residential fires.
This is why arc-fault breakers are being required on bedroom circuits of new construction.

Thanks, AF are for use in residential.

Not obvious to me why a bedroom would be prone to electrical faults that involved arcing more than any other room. Electric blankets? I'll look for them if I ever buy a newer home.

Just a couple of passing thoughts and observations on why AFCIs are being required on bedroom circuits rather than others;

More lamps, clocks, radios, TVs, computers, etc. More extension cords. More overloaded outlet 'multipliers'. More cords run underneath carpeting. More plugs that are damaged by furniture being shoved back against them.
Statistically, more fires start there.
Also, there's less chance of getting out safely if you wake up to a bedroom filled with smoke than if you get woken up by a smoke detector going off in another part of the house.

Some jurisdictions require Arc Fault protection in only bedrooms (older NEC version) and some require it in "family rooms, dining rooms, living rooms, parlors, libraries, dens, bedrooms, sunrooms, recreation rooms, closets, hallways, or similar rooms or areas" (newer NEC version).

It is unlikely that a replacement breaker would need to comply but the only people who can reliably tell you is the local electrical inspector or an electrician.

Arc Fault breakers also have a GFCI function built in, it is just not as sensitive as a real GFCI breaker (0.005 amps).

The warning time for fires in bedrooms is greatly reduced, thus the initial push to get AFCI devices on BR circuits.

Interesting, I would assume the AFCI is more complicated if it can detect an (sudden? what, does it just trip faster when the CB limiting current is hit?) Arc, and imbalance e.g., 5 MA. That noted/assumed I find it strange that Lowes offers a 15 amp AFCI for several dollars less than the 15 amp GFCI.

I'll take a closer look a the CB that went bad, I just assumed it was a GFCI as it fed a bathroom circuit - but strangely (to me) the failed CB has two (White) ground wires coming out of it.

The gfci function is actually pretty easy to create.

Both conductors are passed through a single toroid pickup coil.
If the currents are equal the toroid has no induced voltage (the magnetic fields cancel) and nothing happens.
If the fields do NOT cancel a triac is used to open the circuit.
The sensitivity is as simple as how many turns on the toroid the sense winding has. More turns, more sensitive (less current imbalance).
AFCI devices look for the high frequency noise generated by an arc.
It will be at a multiple of 60 Hz, so filtering is not that hard.
You need to consider that an arc generates electrical noise form the frequency of the voltage to light (the arc itself).
The noise twice a cycle as the arc starts and stops with the 60 Hz voltage.
Sense the noise, turn off the circuit.

AFCI devices are not required to be as sensitive to current imbalances GFCI devices.

Arcs do not trip a CB since the current does not exceed the CB rating.

An arc from a break in the hot line is going to the hot line.
TThe load on the circuit limits the currents, but the arc produces very high temperatures.

A fault is when the hot shorts to the neutral (or ground) and the current exceeds the CB rating.

Breakers for residential use are thermal-magnetic.
The thermal is from heating of a section of conductor in the CB.
This allows brief overloads to pass without tripping the CB (like 'slo-blo fuses). A motor starting or heating elemt turning on are allowed to operate since the current falls quickly and fails to trip the thermal overload.

The magnetic occurs for 200%+ current and results in a very fast operation. The higher the current the more magnetic force is generated and the faster the breaker opens.
At very high overloads the breaker opens in just a few milliseconds.

People are not very good conductors.
You are very unlikely to ever pull enough current through your body to trip the breaker.

Congratulations on a successful job - nice you had some expert help, electrical work has to be done correctly to be safe.

Yes, the Circuit Breaker defines how much power one can draw fom it circuit. I'm not sure why you had a ground fault breaker, but the "more the merrier" I guess as far as this type breaker is concerned - they do provide personal (you) protection in addition to protecting the wiring/building.