I once tried to create an interesting trivia question, where cheating with Google wouldn't help you. I think I did rather well. I do realise that posting this question here completely defeats the purpose, since Google will probably find this question afterwards. (The things we do for fake internet points..) But anyway, here's the question:
Hint 1, from the comments: (won't give away much, but spoiler tagged anyway)
a Golden Lab does not share this connection, and neither does a Blue Whale.
Hint 2: (I can't set a bounty until overmorrow, but at least I can keep this question active.)
The connection is purely nominal.
Hint 3: (wasn't needed by RaT, who solved the puzzle already (wow!), but will come handy if you want to try to solve the puzzle yourself)
Actually, no other animal species shares this connection, at least as far as I can tell.