They are close, but not quite the same.
If a person is sociable, they are able and willing to communicate and seek and/or desire the company of others.
If a person is communicative, it means that they are willing and able to communicate. It does not necessarily say anything about companionship.
For example, a prisoner under questioning might be communicative - willing to talk to police. However, that says nothing about his desire for companionship, though that might indeed be the case.