A is incorrect: Euclidean Distance measures the straight-line distance between two points in a space, reflecting magnitude rather than just orientation or semantic similarity.

B is incorrect: Manhattan Distance (or L1 distance) measures the sum of the absolute differences of their Cartesian coordinates, which is not ideal for semantic similarity of high-dimensional embeddings.

C is correct: Cosine Similarity is the most common metric used to measure the angular difference (orientation) between high-dimensional vectors, which directly reflects their semantic similarity.

D is incorrect: Hamming Distance measures the number of positions at which corresponding symbols are different, typically used for comparing binary strings or sequences, not for continuous vector similarity.