"Good Luck" and "All the Best" Differences

Hello, and thank you for your question!

The phrases 'good luck' and 'all the best' are similar in the sense that they are both expressions of goodwill, however there are slight differences.

1. 'good luck' is often used to wish someone good fortune in a specific endeavor or situation, but it emphasizes the idea of luck playing a role in the outcome.
2. 'all the best' is a bit broader and not as specific. It conveys good wishes for someone's over-all wellbeing and success, and it's often used to give general encouragement, like the teacher did to all the kids before their performance. 

I hope that this gives you some idea of how to use these two phrases.