Best, average, and worst case describe one algorithm running on different inputs. Worst case is the slowest an input can make it. Best case is the luckiest input. Average case is what you expect over typical data.
Take searching an unsorted list for a value. Best case, it sits first, so O(1). Worst case, it sits last or is missing, so O(n). Average case lands around the middle, still O(n).
You usually plan around worst case because it bounds the pain. Best case is often useless for guarantees. Average case matters when you know the data behaves normally and rare slow inputs are acceptable in your system.
Rewriting in plainer words…
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