Each system has its own creation story, often a monk or a famous general or an outlaw who had some inspiration or other that helped them create a new system. Those stories should be taken with a grain of salt, as they are often embellished a lot. There may be some truth in them, or none at all, but as a creation mythology they give an identity to the system and those who practice it. Of course these stories often have a founder who was unbeatable once he created his new method, and used the system to overcome an adversary of some kind. My own system is traced back to a Tibetan lama who witnessed a fight between a crane and a large monkey, by a mountaintop lake. This gave him inspiration to develop a new methodology. The story is actually plausible, the elements exist and could have happened, but the story traces back to the 1400s, so I personally do not believe it happened exactly as it is told.
These things are often linked to a monk or mysterious hermit or a famous general. Nobody wants to know that their system was actually created by the village drunken outhouse cleaner. So if the origins are sufficiently obscured in history, well the story might change a bit.
Animal systems, in my experience, are more focused on deeper principles of movement and application, and are less about specific techniques that mimick animal. Those techniques do exist, but they are often not as heavily used as people seem to assume. Nevertheless, they can become the "signature" move of the system, at least as far as the uneducated public understands it. But the reality is often not that at all.
For example, in my own white crane method, our use of the single leg stance is rare and usually very brief and simply a step as transition into something else. Our use of the crane beak strike is also rare, and when it is used is often applied as a hooking movement rather than a strike. So, no, in white crane we do not stand on one foot and poke at people with our finger tips. Nor do we flap our arms like wings.