There are no icons to designate anything to do with animals, pets, and care. |
http://wiki.openstreetmap.org/wiki/Map_Features should be in your bookmarks. Not all tags are rendered but the tag will be there. |
I guess you refer to the Potlatch2 (aka 'P2') editor icons. Those are predefined tags easy to handle but OSM is much more. Also the online map you see on the main page is only rendering a part of the data. |