"Ideal state of mind" will be relevant to the situation, sometimes that's quietly relaxed... sometimes it's chanting with the crowd to motivate your team, sometimes it's letting go to laugh at a comedy, sometimes highly energised like for sports. It's the mind set you've discovered that helps you bring about the best results.
Consider it a fexible term to mean a state of mind that works best for you and most appropriate for what you are about to do.
"Relaxed state of alertness" is exactly that, the state as described. It's best uses are when you want to be there listening, watching, learning, doing or paying attention to what is happening within or in front of you.