In Quick Sort, we sort the array by selecting a pivot element and partitioning the array such that all elements smaller than the pivot are on its left and all elements larger are on its right. This process is repeated recursively for the subarrays on either side of the pivot until all elements are in their correct positions relative to each other. Through this process, the entire array gets sorted without requiring any additional array, as the sorting is done in-place.

In Merge Sort, the array is divided into two halves recursively until each half contains a single element or is empty. Then, the sorted halves are merged together by comparing elements from each half and arranging them in sorted order. This process continues until the entire array is merged and sorted. Unlike Quick Sort, Merge Sort requires additional memory to store temporary arrays during the merging process.