There is a big difference. To be shy means timid and reserved in the company of others, while ashamed means to feel a sense of shame about oneself or something one did.

Is shy and shame the same?

shy is used for someone who its scared or afraid but only to a little amount. "she was shy because she was going to meet new people". shame is used when you feel bad or hated for doing something. "you shamed yourself for accidentally screaming in the library"

Does embarrassed mean shy?

“Shy” would imply that he was afraid to tell her because of a fear (rejection or something else). “Embarrassed” implies that he wasn't afraid, but feels vulnerable saying so.