모으다 : pure Korean word 저축하다 : chinese characters(저축) Usually, pure Korean words have more comprehensive meanings. Words made of Chinese characters have more specific meanings.

돈을 모으다 : to gather or save money 돈을 저축하다 : to cut down on expenses and save money When you say '저축하다', it is more likely used 'to save money in bank accounts'. 저축하다 can be included in the meaning of 모으다. Hope it helps and please follow me at koreanclass.canada on Instagram!