It can definitely get confusing! 
General Terms
A dimmer module controls the light by varying the current level sent to the fitting. It can only be used with fittings that have nonnetworked dimmable lamps.
A relay controls the light with a simple on/off of the current. It is compatible with a wider range of lamps and Devices.
A “dual” Version of a relay is a single box which can be wired to two separate devices. For example, if you had a bathroom switch that had an on/off button for the lights and an on/off for an extractor fan, you might be able to use a dual relay behind the switch to give you automated control of both.
Fibaro’s Terminology
Different manufacturers do use slightly different terms for their own models. Sometimes this is a matter of translation if a manufacturer is headquartered in a different country and the English name is a translation of the original name. Sometimes it’s just a style choice.
Fibaro uses the term “Switch” for their relays, whilst most manufacturers use “switch” for both dimmers and relays, they just put “dimming” in the name of the model which can do dimming.
Fibaro uses the term “double” where most manufacturers use the term “dual” but they mean the same thing-- a single box which can control two devices.
Fibaro added a “2” at the end of a device name when they added their own second generation of a device. So a “dimmer 2” (FGD212) is the newer version of the original “dimmer” (FGD211), but not, as you noted, a dual device – – the dimmer can only control one fitting.
Fibaro 222 vs Fibaro 223
The 223 is a newer model of the 222. There are a few differences, but you have to dig down into the fineprint technical specifications to find them. In terms of basic functions they do the same thing: each is a relay (on/off switch) which can control two different devices.
Z-Wave Fibaro Double Switch 2 GEN5:
“GEN5” on a Z wave device usually refers to the technical specifications of the Z wave chip inside the device. The newest version is “Z wave plus” which was the fifth generation of Z wave, so it is also referred to as “GEN5” and “Series 500.” When compared to the previous versions of zwave, zwave plus Devices have better range, easier pairing in place, better battery life for battery powered devices, and typically a smaller form factor. All of these together were important enough that this generation even got its own logo.
As far as for Fibaro – specific changes, when compared to the 222, the 223 has an indicator diode for diagnostics, allows connection with a larger size of wire which lets it be installed in more places, added some more safety features and notifications, but dropped the dry contacts (potential free) feature which you won’t need just for lighting but was used for some other types of applications.
At this point (August 2017) many retailers have sold out of the older generation, so it is becoming more difficult to find. The newer generation, the 223, is widely available.
@anon36505037 has done his whole house with Fibaro micros, so hopefully he will chime in.
But the short answer is that the manufacturer intends the 223 to replace the 222. The 223 is a newer version and is zwave plus. But there are some features on the older 222 which are desirable for some kinds of projects, so you will still see posts about people using the 222 as well.
