A studio album is an album created in a studio, as opposed to someone's bedroom, bathroom, or just out in the woods.
In olden days, all albums were recorded in Churches, to make certain no evil messages from the devil got into them, as was a growing concern for parents way back in the 1980's. It was believed that children might play a record backwards and receive a hidden message commanding them to be evil, and this message was so powerful that all the years of raising them proper would be eliminated instantly. Some said bad parents were just desperate to find a scapegoat so not to blame themselves for their children's behavior, and since video games weren't violent enough to blame on anything back then, they had to blame music instead.
To see a list of Taylor Swift's studio albums, see albums. You can be assured that are of them are made with her angelic charm, and are safe for children to listen to.