"바꾸다" is a transitive form, it needs the objective in the sentence. In fact, most of sentences you use are active. For instance, I'm going to change my swimsuit, it's quite old. -> 저는 수영복을 바꿀려고 해요. 꽤 오래됐거든요. I'd like to exchange dollars to euros. -> 달러를 유로화로 바꾸고 싶어요.(or 환전하고 싶어요) Meanwhile, "바뀌다" is an intransitive and a passive form. It doesn't need the object in the sentence. For instance, The world is changing so fast, full of digital gadgets, sometimes people miss analog. -> 세상은 빠르게 바뀌고(or 변하고) 디지털 기기들로 넘쳐나지만 사람들은 가끔 아날로그를 그리워해요. He has totally changed. So kind and positive. -> 그는 완전히 바뀌었어요. 정말 친절하고 긍정적이에요.

I will tell you a real story. Two friends CHANGED their application forms of universities. (두 친구가 대학교 입학원서를 바꿨습니다./'바꾸다'의 예) They entered the universities they applied. Their lives CHANGED at the time when they changed the application forms. (두 사람의 인생이 바뀌었습니다./'바뀌다'의 예)

바뀌다 is passive form. it's hard to explain in English. but i can show you some examples. "선생님이 마음에 안 들어서 다른 선생님으로 바꾸고 싶어." I don't like my teacher so wanted to change another teacher. 내가 바꿀 수 없으니가 저절로 바뀌면 좋겠다. I cannot change the teacher so it is changed naturlly