All GFCIs may be differential CBs, but not all differential CBs are GFCIs.
The term GFCI indicates specific current thresholds, 6ma for Class A.
Yes, correct. But more specifically:
There are potentially confusing terminologies for all of this stuff collectively called "Ground Fault" equipment here in North America but with other terms from different areas of the world.
In Europe and Asia, they use the term Residual Current Device (RCD) or Residual Current Circuit Breaker (RCCB). And RCD does not have the CB current sensing, just the differential.
In South America, Brazil in particular, some people call them Differential Residual (DR) or Differential Current (DI, because I = Current) circuit breakers. Weg, a large Brazillian supplier, has begun exporting their components here to the US in recent years and their DR breakers are showing up in catalogs and stores, then get misapplied by sales people who have no clue.
Here in North America, we call these types of devices Ground Fault Protection for Equipment (GFPE) devices or Equipment Protective Devices (EPD). Their intent, as far as North American standards, is for EQUIPMENT ground fault protection, NOT personnel ground fault protection. RCD, RCCB, DRs and GFPE devices can have a trip threshold of anywhere from 30-500mA of ground differential current.
In North America when it comes to protecting PERSONNEL from electrocution, we require a much much LOWER trip threshold of 5ma (at least 4, no more than 6mA) and to differentiate them from GFPE devices, we very specifically refer to them as Ground Fault Circuit Interrupters (GFCI). GFCI is a very specifically DEFINED term in both the NEC, UL and OSHA regulations, it means only this one thing.
In other countries, 30mA is considered acceptable for life-safety protection of personnel in wet areas. That, in combination with our use of GFI (see below) and lazy people just calling this "Ground Fault" devices,
leads some international suppliers to mistakenly sell their RCD type devices as "Ground Fault Breakers", allowing North American users to ASSume they are the same as GFCIs. They are NOT.
GFCI = North American device for protecting PERSONNEL from electrocution in wet environments, 5mA trip level. Could be a wall device, a receptacle with it built-in, or a circuit breaker. Also called a "Class A Ground fault Device"
GFI = older term for GFCI, but NO LONGER officially recognized because of confusion with GFPE. I think that originally a GFI was a receptacle ONLY, it did not protect devices down stream of it. GFCIs are now required to do that, so there are no GFIs any more. Some people however still use the term, claiming it is synonymous to GFPE. I'm not clear on that distinction.
GFPE = 30-500mA differential trip level (if differential) on up to a percentage of rated current (Zero Sequence) for protection of EQUIPMENT only, aka EPD, and elsewhere in the world, RCD, RCCB, DR/DI circuit breaker. Could be a stand alone device or as part of a circuit breaker. GFPE at the 20-30mA level here in NA is also called a "Class B Ground Fault Device" and has specific call outs in the NEC.
Other terms:
RCBO = In the UK, an RCD + a regular CB together, our equivalent to a GFCI CB, other than the trip level issue.
ELCB = Earth Leakage Circuit Breaker (or ELCI, for Interrupter), and older term for RCDs, although ELCBs were not always differential, some sensed voltage.