plover, (kokuji)
鵆 centers on a specific bird: the plover. It is a kokuji created in Japan, so its meaning is tightly tied to that one bird.
鵆 is a Japanese kokuji, combining 行 (going) and 鳥 (bird) to represent the plover, a bird known for its quick running along the shore. The character was likely created to give a native Japanese word a kanji form.
A bird 鳥 that is always on the go 行 along the beach: that's the plover 鵆.
For ちどり, picture a plover running so fast it looks like a thousand 千 (ち) birds 鳥 (どり) darting along the shore: 千鳥 -> ちどり.