They are different words. The two words were originated from Chinese. 감 means "to feel; to move; to touch; to affect; feeling; emotion" 동 means "to move; to set in movement; to displace; to make use of" 정 means "feeling; emotion; passion; situation" 감동 means "to move (somebody); to touch (somebody emotionally); moving" 감정 means "feeling; emotion; sensation; likes and dislikes; deep affection for somebody or something" 감동 mainly used as a verb with "하다,시키다" ex) 나는 그 소식을 듣고 크게 감동했다 I was deeply moved at[by] the news. 아내의 정성이 그를 감동시켰다 His wife's sincerity[devotion] touched his heart. But also can be used as a noun. ex) 그녀는 그의 이야기에 감동의 눈물을 흘렸다 She was moved to tears by what he said. 나는 그녀의 말에 깊은 감동을 받았다 I was very[deeply] touched by her words. 감정 always used as a noun. ex) 그는 감정이 메말랐다 He has no emotions at all. 그는 감정 표현을 거의 하지 않는다 He hardly expresses[reveals] his feelings.

Both seems quite different for me. Even though both are related to the meaning of emotion, I can't think of it as a synonym. 감동 is more like touched or moved by sth. 감정 describes a feeling itself. ex) 너가 나를 위해 음식을 만들어줘서 감동 받았어. 연극은 참으로 감동적이었어. // 나는 요즘 감정적으로 힘들어. 너는 감정 기복이 심한 아이구나. 내 감정은 고려하지 않고 니 멋대로 행동해서 화가 나.