cat
貓 centers on the animal cat. It is the traditional form of 猫, carrying the same core meaning.
貓 is the traditional form of 猫, combining 豸 (beast) with 苗, which likely provides the sound. The modern simplified form 猫 uses 犭 (dog) instead of 豸, but both forms refer to the cat.
The left side 豸 suggests a beast, and the right side 苗 looks like a seedling in a field. Imagine a cat prowling through a field of seedlings, hunting like a small beast.
For ビョウ, picture a cat letting out a soft 'byou' sound as it pounces on a toy mouse: byou -> ビョウ, and the cat's hunting instinct matches the beast radical.