Both n log n and n are commonly used to analyze the time complexity of algorithms, with n log n usually indicating a more efficient algorithm.

n represents linear time complexity, meaning that the time required by the algorithm increases linearly with the size of the input. For example, an algorithm that simply loops through an array of n elements and performs a constant-time operation on each element would have a time complexity of O(n).

On the other hand, n log n represents a sub-quadratic time complexity, which is faster than linear time complexity but slower than constant time complexity. It often appears in divide-and-conquer algorithms, such as merge sort or quicksort. These algorithms divide the problem into smaller subproblems and recursively solve them, and then combine the results.

For small values of n, the difference between n and n log n is small. However, as n grows larger, the difference becomes significant. For example, if n is 1,000,000, then n log n is approximately 20,000,000, while n is simply 1,000,000. This means that an algorithm with n log n time complexity will be significantly faster than an algorithm with linear time complexity for larger inputs.

In summary, n log n represents a more efficient algorithm than n for larger inputs, but n may be sufficient for smaller inputs.