It looks like there are at least two different badges where where addons can have different meaning. But the first rule is common -- you need gem level to get addon:
When achieving the status of a Gem badge you have unlocked the possibility of Addons.
One of them is described in the wiki. It makes sense for types badges:
For example, The Traditional Cacher will get a nice 366-addon added to it if you have logged a Geocache of the type Traditional on every date of the calendar.
Example with Climbing addon will be similar as your Boat example. It is described in this answer. To get the addon for climbing gear, you need to have at least the diamond requirements fulfilled with caches having Climbing or Boat attribute (for Rugged Cacher and Climbing, it is 150).
Other example are FTF, Leap day and so on. These really can not require to have hundreds FTFs on this type of caches or on this day so they look like require just one of these.
But I agree that this would be nice to have summarized in the wiki and confirmed by somebody who wrote the code or has more knowledge about the system.
