What is the national animal of Russia?

Russia's national emblem is listed as a double-headed eagle. However, foreign western countries generally compare Russia to a grizzly bear. The following memory is a bit vague, so it cannot be guaranteed that 100% is correct. My memory seems to come from an autobiography of Churchill. He once had a meeting with Roosevelt Stalin. Afterwards, when describing the meeting, he said that he was sandwiched between an American bull and a Russian grizzly bear (trying to survive among big countries) and became a poor little donkey.