Shoulder height and other conventions
There is no universal way to measure an animal. There is a set of conventions, each one chosen because it is repeatable on a real body, and the conventions differ from species to species in ways that look arbitrary until you try to do the measuring yourself.
The test every convention has to pass
A measurement convention is not chosen for elegance. It is chosen because two people with a tape measure and the same animal should get the same number. That single requirement explains almost every convention that looks strange from outside.
Take an elephant. Measuring to the top of the head sounds natural and is useless, because an elephant's head moves through nearly a metre of vertical range depending on what it is doing. The shoulder does not. So elephants are measured at the shoulder, and an African bull comes out at 3.2 m. That is 1.87 times a person at 1.71 m, and the figure is stable enough that two zoos will agree on it.
Bison, and the hump that is not fat
American bison are measured at the shoulder as well, but the shoulder of a bison is a pronounced hump built from elongated vertebrae and the muscle that drives the head through snow. The measured figure is 1.75 m, and the animal's actual highest point when it lifts its head is well above that.
The convention survives because the hump is skeletal. It does not move. Anything that does not move makes a good measuring point, which is the entire principle in one sentence.
Withers, shoulder, head. A horse is measured at the withers in hands, an elephant at the shoulder in metres, a great dane at the shoulder in breed standards. The Great Dane figure used here is 0.98 m to the top of the head, roughly seventeen centimetres above the breed-standard shoulder measurement. Against a miniature dachshund at 0.38 m that gives 2.58, and the same comparison taken at the shoulder on both animals gives a different answer.
Bears, and the two-figure problem
Bears are the clearest case of one animal with two published heights that differ by a factor of two. The figure used on this site is 2.5 m for a grizzly, which is the animal upright on its hind legs. On all fours the same bear stands roughly 1.2 m at the shoulder.
Both numbers are correct and they answer different questions. The upright figure tells you how high the animal can reach. The shoulder figure tells you how big it is as a body. Popular writing tends to quote the first and illustrate the second, and the result is a persistent overestimate of how large a bear looks walking.
Polar bears get the same treatment with an extra twist: the figure used here is 2.5 m, and it is a length, nose to tail on all fours, not a height. Against a white rhinoceros at 3.7 m, both measured as body lengths, the comparison is clean. Against a standing grizzly it would not be, because one number is a height and the other a length.
Gorillas and the knuckle-walking problem
A gorilla's stated height of 1.3 m is a standing height at the shoulder of an animal that moves on its knuckles. That is lower than most people expect, because the mental image is of a gorilla upright, which is a posture they adopt briefly and for display.
The convention here matches how the animal is normally seen. Set against an emperor penguin at 0.95 m, measured standing upright to the top of the head, the ratio is 1.37. The penguin's convention and the gorilla's are not the same, which is exactly the kind of thing worth saying out loud rather than hiding.
Reptiles are easy, which is why they are useful
Crocodiles and lizards are measured snout to tail tip, total length, and the convention is almost never disputed. A saltwater crocodile at 4.5 m and a Komodo dragon at 2.4 m are both total lengths, and in both cases roughly half the animal is tail.
That consistency makes reptiles unusually good reference objects. A crocodile at 4.5 m against a person at 1.71 m mixes a length and a height and therefore needs the caveat, but crocodile against crocodile, or Komodo dragon against bearded dragon at 0.5 m, is as clean a comparison as the catalogue offers: same convention, same posture, ratio of 4.8, nothing to argue about.
Birds have three conventions and use all of them
Standing height, body length and wingspan are all in circulation for birds, and which one is quoted depends on the bird. Ostriches are quoted standing height, 2.4 m, because they are famous for being tall. Condors and albatrosses are quoted wingspan, 3.2 m and 3.11 m, because they are famous for flying. Chickens are quoted standing height, 0.35 m, because that is how you see them.
The result is that two bird figures in the same sentence are rarely comparable. An ostrich at 2.4 m standing and a condor at 3.2 m spanning are not describing the same kind of distance at all, and there is no honest way to say which bird is bigger from those two numbers alone.
The general rule
Where a species has a published convention, follow it. Where it has two, say which one you used. Where it has none, pick the dimension the animal is actually described by in ordinary speech, because that is the one a reader will picture.
What you must not do is switch conventions inside a single comparison to make a number look better. That is the difference between a measurement and a claim, and it is the reason every page on this site names the axis and states what the figure covers before it states the ratio.