what is difference between database developer and administrator?
At a masters level you should be pretty good at both  

Administrator - DBA 


install and configure hardware
maybe you say that is outside of DBA but most DBA can do hardware   
install and configure database software  
optimize the database configuration  
users, groups, and security 
backups 
index maintenance   
monitor 
need basic SQL just to query systems tables and validate data  
build tables and indexes


Developer  


database design  
write, queries, procedures ....
index planning and implementation  
build tables  
performance monitoring 


Mix 


if you get into partitions and other exotics the database design gets into hardware  
index maintenance - if the DBA is going to do this need to understand indexes
data load - is this a DBA or developer?
if it is the DBA then need a lot of developer skills  


At a master level should know at least one language / platform.  If you load data there going to be times you need to scrub it row by row.

In a large software shop you may have a developer on a programming team that really only does pure development.   Lets say you are running a packaged application like SAP you would have a DBA that only does DBA and not even have a developer. 

Also have application developers that are also database developers.  For big high volume applications the back end developer(s) need to be part database developers.  For small apps that cannot afford a database developer the application developer has no choice but to do it all. 

If you are a DBA expect to do some mail, web, group policy, and other system tasks at some point in you career.