Both "이를 닦다” and “양치하다" have same meaning. 이를 닦다 is pure Korean phrase. it is more commonly used in spoken language and informal situation. 양치하다 is Sino-Korean phrase. it is more commonly used in written language and formal situation.

양치(養齒)하다 is from Hanja/Chinese. So its slightly more formal than 이를 닦다. Parents will use 양치하다 with their kids but you'd use 이를 닦다 with your friends unless you're in a formal situation.

"양치하다" and "이를 닦다" have same meaning, 'brush the teeth' even though they look different :)