Well your answer can easily be found by reading the Wikipedia entry for 'ladybug.' But since I'm feelin' helpful I'll just tell you what's what.
The name ladybird originated in the UK. It was originally called 'Our Lady's bird' or the 'Lady beetle.' Mary (the virgin Mary - aka "Our Lady") was sometimes drawn wearing a red cloak in the early religious paintings. Ladybugs are red. The spots of the ladybug (the most common ladybugs have seven spots) were said to symbolize Mary's seven joys and seven sorrows. In the U.S the term was adapted erroneously to just ladybug, even though it's not a true bug.
And there you have it. The ladybug, or ladybeetle, or ladybird.