Ultimately, it's just a name, but you're right, the convention is 2 is "bigger" than 1. Let me explain.
WIDE2 stations tend to cover a wide area and often have Internet connections to send the reports along. WIDE1 stations usually cover a smaller area fill in the gaps between WIDE2s (there can be lots more of them.) They typically pass the packets along to a WIDE2.
A reporting station will have a routing path. A path for a fixed station will typically be WIDE2-2 because it will usually be within reach of a WIDE2. Passing its packet to a WIDE1 would just add useless traffic.
Mobile stations may not be so lucky to reach a WIDE2, but could likely reach one of the WIDE1s. With a path of WIDE1,WIDE2, the mobile stands a much better chance of having his packet passed along.
As for "who digipeats it", any station configured to handle WIDE2 packets will repeat it. Usually the community at large will agree on which stations are the WIDE2s so you don't have a channel full of them. "How often" is a configuration setting, and "How far" depends on its RF reach and whether the station is connected to the Internet.