Why are Coccinellidae known as both ladybug and ladybird?

Ladybird is the name for the insects in the Coccinellidae family. In the USA, Coccinella septempunctata, the specific red and black ladybird is called a ladybug.

Ladybird is a name that has been used in England for more than 600 years for the European beetle Coccinella septempunctata. As knowledge about insects increased, the name became extended to all its relatives, members of the beetle family Coccinellidae. Of course, these insects are not birds, but butterflies are not flies, nor are dragonflies, stoneflies, mayflies, and fireflies, which all are true common names in folklore, not invented names. The lady for whom they were named was "the Virgin Mary", and common names in other European languages have the same association (the German name Marienkafer translates to "Marybeetle" or ladybeetle).

https://entnemdept.ufl.edu/creatures/beneficial/lady_beetles.htm

The coccinella was named lady"bird" because it could fly. One theory is that the US call is lady"bug" because we call all insects bugs... While one could argue that beetles are not really bugs it could be said they are closer to bugs than birds...

https://grammarist.com/interesting-words/ladybug-and-ladybird/