In the modern anglosphere, a good way of pointing out how smart you are is pointing out that monkeys and apes are two different things-but the distinction between the two is fairly recent--most species of ape not being officially discovered until after the middle ages, (Gorillas weren't discovered until 1902!) and romance languages do not have a separate word for the two. The word "leopard" is a compound word of leo (lion) and pard (panther), as people in the middle ages thought the the leopard was a hybrid beats of the two--not realizing panthers are not even a species in their own right, but a phenotype for big cats.
When society collapsed, several beasts escaped from zoos, preserves, and private collections. A great deal died out, or were hunted to death, but in the fringes, a few of the big cats lasted long enough to leave impressions in people's minds. Due to rare sightings, and perhaps even the occasional cross-breeding, the line between the big cats have blurred a little. The general rule of thumb is that "lion", or its equivalent, may refer to tawny cats found in the arid west. These may include the African lion which has found a home in the Baja peninsula, or more commonly, the "mountain lion", or cougar, In fact, the layman may assume the two are the same animal, and cougars are merely the mates or children of the "king of beasts". Meanwhile the "tiger" is applied to cats with very visible patterns--and can be applied to actual tigers, bobcats, ocelots, and even jaguars. "Panther", of course, still refers to large black cats, though they're almost never seen in America.
In the former U.S., lion imagery is much more popular in the west, due to presence of outright monarchies, and that cougars are a visible part of the landscape. In the East, however, tiger imagery is favored, as Warlords don't want to evoke regality so much as power. The flag of Ohio is probably technically a liger or a tigon, and the rules will use the words interchangeably as needed. Panthers tend to pop in heraldry in places with historically large black populations.