How does K$-$Means clustering differ from Mean Shift clustering?

Group of answer choices:

$1)$ All of these are correct.

$2)$ K$-$Means requires the number of clusters to be specified in advance, while Mean Shift automatically determines the number of clusters based on the data distribution.

$3)$ K$-$Means uses centroids that are updated by minimizing intra$-$cluster variance, whereas Mean Shift relies on density gradients to shift points towards higher density regions.

$4)$ K$-$Means is sensitive to initial cluster centroids and may converge to local minima, while Mean Shift is less sensitive to initialization as it operates based on local density peaks.