Brits call them ladybirds, Americans call them ladybugs. Where did these two names come from?

Many years ago, it was once believed that ladybugs came from heaven to save farmers' crops. The farmers called the insects 'the Beetle of Our Lady' or 'Virgin Mary's Gold Hens,' in dedication of the Virgin Mary.'
[discoverlearning.com/webjourneys/ladybugs/step2.html]
http://elysiumgates.com/~mamawolf/facts.html

I found a number of other sites that listed the 'Beetle of our Lady' answer to the ladybug question. The only reference I found to the bird part was at www.dictionary.com where it says that they were also called 'Bird of our Lady,' though no explanation is given. It also says they are called Ladyclocks, lady cows, lady flies, and lady beetles.