What Is a ‘Morning Star,’ and What Is an ‘Evening Star’?

I once received an interesting inquiry from a woman who wanted to know the meaning of the terms “morning stars” and “evening stars.”  She wrote: 

“I mean, they’re not stars … they’re planets, right? So why do we call them stars? And is a ‘morning star’ only visible in the morning, like at the crack of dawn, or at other times as well? Hope you can clear this up for me because I’m totally confused!”