(someone) is shy

A person who "is shy" is afraid to talk to people who they don't already know well.

Here's an example:

Gene has always been a little shy.

"Shy" is a very common word that you can use in both formal and casual situations.

(someone) is being (adjective)

When someone is acting in a way that's different than how they usually act, you can say that they "are being ___". For example, if one of your children is not cooperating with you, you can say:

Why are you being so difficult?

Or say this about your friend who's getting on your nerves today:

She's being annoying.

There are some adjectives that you don't use with "being". For example, "angry" does not need "being". You can just say:

She's angry.