shy is the same as timid, embarrassed goes deeper than that, comparable to feeling shame in front of others.

Being shy is when you are not feeling comfortable around other people. Usually it's because you don't know the people around you well. Shyness makes one talk little, not very loud, or hide away from the group. Embarassed is when you are feeling unwell around people because you feel judged for something that happened. For instance, if you pants fell down in front of a crowd, you would most likely be embarassed. Shyness tends to be something that a person is from day to day. We says things like "He is very shy." Being embarassed is always the result of something that happened or that one thinks is happening. Hopefully, no one is embarassed all the time.