When I clicked the difficulty button to switch difficulty from casual to challenge, an asterisk was put on it. 

What are the conditions for that asterisk showing up? Is it "the asterisk appears if you've ever won a match in Casual"? Is it "the asterisk appears if there's any match you've won in Casual but not in Challenge"? Or is it something else?

It's for winning any match in Casual, period.

This way, you cannot e.g. get the Efficient achievement in Casual and then go back and replay levels with 100 energy.