In Korea, there is a device called 'Flight data terminal' which enable air traffic controller to get clearance or search certain flight plans automatically. But I found that there is no 'FDT' in western countries. I believe there must be some devices whose functions are similar to FDT of Korea, so I want to know the name of that device.
The European equivalent would be the Flight Data Processing System (FDPS). The FDPS receives flight plans over the Online data interchange (OLDI) / ATS Message Handling System (AMHS) from the Integrated Initial Flight Plan Processing System (IFPS) which is operated by EUROCONTROL. In addition local flight plan can be added to the FDPS.
Aircraft operators file their flight plan with the IFPS, which checks the flight plan for correctness (syntax errors, route errors, etc) and determines whether the plan is acceptable to the air traffic service providers. If necessary, plans are rejected or modified. Once the plan is acceptable, it is distributed to all Air Traffic Control units (ATCU) along the route.
In the ATCU, the FDPS will receive the flight plan and store it in its flight plan database.
It must be noted that the FDPS is much more than just a flight plan database. It is at the heart of the air traffic control unit. It correlates flight plan data with actual radar tracks, updates flight plan with inputs from air traffic controllers and it supports local flow management functions, conflict detection systems and much more.
Without knowing the Korean system, it is impossible to tell exactly what you are looking for. However, based on your minimal description, it sounds like you might be looking for systems like CPDLC or other data link systems. These are not automated systems per se, but simply systems that allow digital, text-based communication between ATC and pilots, instead of VHF-based voice communication.
Automatic exchange of fight plan data is done, in Europe at least, via online data interchange (OLDI).