Amortized time and worst case (non-amortized) separation
Heapify is one example:
https://www.geeksforgeeks.org/time-complexity-of-building-a-heap/
Another simpler example (Min / Max queue):
https://www.geeksforgeeks.org/design-a-queue-data-structure-to-get-minimum-or-maximum-in-o1-time/  . This is also discussed here (see Szymon's answer): https://stackoverflow.com/questions/12054415/get-min-max-in-o1-time-from-a-queue
And there are many more...