What is a adoptees?. On the internet, there are pixel sites that make pixel art. These little pixels serve no purpose aside
from being cute decoration, when one downloads these pixels to decorate their site, they "adopt" the pixel (because most pixels are animals/people).
What is a claim? Again, on the internet there are many fansites that offer "claims" of anime/manga/game characters, celebrities and even songs for fun.
The majority of these sites are fansite dedicated to a specific fandom (ie. One Direction, Bleach, Pokemon), the claim badges are similar to adoptable pixels that serve
as decoration or declaration of being a fan like a button of a fanlisting.