O(log n) and O(n log n) are both logarithmic-based time complexities, but they represent different levels of efficiency. O(log n) indicates that the runtime grows logarithmically as the input size increases and is typical of divide-and-conquer algorithms like binary search, where the input is halved at each step. O(n log n) is commonly found in algorithms that perform an O(log n) operation for each of the n elements, such as merge sort or quicksort. While both are efficient, O(log n) is much faster than O(n log n) for large inputs. Understanding these time complexities helps in selecting the right algorithm for a problem based on its input size.