Kris Johnston said in a comment:
nomount/mount/open are the states of the database... something can't connect to the db one way and connect as nomount, and connect to the same db a different way and connect as mount or open. It doesn't work like that. It sounds like you are connecting to a different database altogether. To check, verify the dbid's are the same/different when you connect via RMAN. Also, instead of connecting to rman, connect to sqlplus using your various connection methods, then check: select status from v$instance; select dbid from v$database; (have to bring the db into mount state to query v$database).
Issue has been fixed. Kris, your explanation actually made sense, I am not sure why, but there were multiple Oracle instances running in top for the same database, so I had to kill all those and use the same SID strings in the scripts, with the exact case, and everything worked fine.