Question: OK when working with table creation, is it always assumed that creating a table on one database (the master) mean that the DBA should create the table on the slave as well? Also, if using a master/slave configuration, shouldn't data always be getting replicated from the master to the slave to synch? 

Right now the problem I am having is my database has a lot of stuff in the master, but the slave is missing parts that only exist in the master. Is something not configured correctly here?

Answer: 
I prefer to rely on `CREATE TABLE` statements being replicated to set up the table on the slave, rather than creating the slave's table by hand. That, of course, relies on the DBMS supporting this.

If you have data on the master that isn't on the slave, that's some sort of failure of replication, either in setup or operationally.
Any table creation on master is replication on slave. Same goes with the inserting data. 
Go through the replication settings in my.cnf file for mysql and check if any database / table is ignored from replicating.