As SMOE is part of EPIK, if you are interested in applying to SMOE you will have to apply to EPIK. You can apply to EPIK, GEPIK, GOE at the same time however each program will require you to submit a set of documents when securing a position.
Sources
- EPIK 공식 사이트 — EPIK / English Program in Korea (국립국제교육원)