특별히 is like 'specially' The ring was specially made for her. 특히 is like 'especially' She loves all sports, especially swimming.

특별히: particluarly, specially, 딱히 특히: especially 지금은 특별히(딱히) 먹고싶은게 없다: There is nothing particular I want to eat right now. 이 학교 선생들은 짜증난다, 특히 음악선생이 완전 꼰대다: The teachers at this school are annoying, especially the music teacher is a complete #$@#.