Dear Lakshay Sharma,
Yes. your point is right. Embedding in Skip gram it is more about the meaning of that word like what "am" is used for.
The CBow is better at capturing contextual co-occurence, and The Skip-Gram is to learn deeper semantic relationships between words.
reference: https://medium.com/@RobuRishabh/learning-word-embeddings-with-cbow-and-skip-gram-b834bde18de4