Yes, the maps are different.
"Garmin Cycle Map" is Garmin's version of maps based on Openstreetmap (OSM) data. The City Navigator (CN) maps are based on other data (Garmin/Navtech).
The same OSM maps are provided with the 1000/1000 Explore/Touring units. I'm assuming the routing works the same on all the units (I'm more familiar with the Touring).
Yes, they come with a regional map (I don't know if the UK units come with all of Europe).
You can't buy or get the Cycle maps other than getting them with a unit (as far as i can tell).
But it shouldn't matter too much, especially if you are using loaded routes, since there are many sources for Openstreetmap based maps.
It might matter more when you have the device generate routes (not using a loaded route) since other sources of OSM are compiled for the 800/810, which have somewhat different routing parameters.
The significant issue is that the Touring doesn't deal with "highways" (the 800/810 do). Some of the cycle OSM maps classify cycleways as "highways" which might make them not available to being used for routing on the Touring. People in the UK (in particular) can get odd long-way-around routing when using the Garmin Cycle maps because round-abouts on A roads are classified as "highways" (A roads and the round-abouts on them are classified as "highways". In the US, highways are more like M roads. (Oddly, there A round-abouts are not classified as "highways" on the CN maps.)
The Touring allows (maybe, the 1000 does too) you to generate routes based on elevation data in the "dem" map that comes with the units. I don't know of a ready source for those maps.
Using loaded routes (planned on something like ridewithgps) will tend to be more predictable than generating routes on the device (true for all of them).
Free worldwide Garmin maps from OpenStreetMap
You can use the CN maps but I don't see a real need to.
Providing OSM lets Garmin sell the units for a bit less (by avoiding the cost of the non-free CN maps). The OSM maps also include cycleways and cycle paths. The CN maps don't (they are more tailored for cars).