I need to transfer some data from another database. The old database is called paw1.moviesDB and the new database is paw1. The schema of each table are the following.
Just like leonbloy suggested, using two schemas in a database is the way to go. Suppose a source schema (old DB) and a target schema (new DB), you can try something like this (you should consider column names, types, etc.):
INSERT INTO target.Awards SELECT * FROM source.Nominations;