I'd always heard (I grew up next to a cow pasture): you want to pet the bull, but run from the bear.
The real origin of the terms is from the early 1700: "seller of the bear skin before the bear is caught" - old proverb - was called the player that tries to deliver goods after their price has fallen (so a seller in advance). In 1709 the term was in fact 'bearskin'.
Ten years later the "bull" was introduced as a counterpart - this time probably with relation to the images.