보이다 is both the passive and the causative form of 보다. - 아이는 학교에서 받은 상장을 꺼내 보였다 - The kid pulled out and showed the award he received in school. - 아이는 오늘따라 풀이 죽어 보였다 - The child looked particularly depressed today. 뵈다 has two meanings: 1) same as 보이다, 2) honorific form of 보다 in the sense of 만나다(meet). - 이렇게 또 만나 뵈니 좋네요 - It's nice to see you again like this. - 지난 번 뵈었을 때보다 건강해 보이세요 - You look healthier than the last time I saw you. 뵈다 seems to be used as honorific 만나다 more often, as we tend to use 보이다 for the passive/causative meaning. Using 보다 instead of 뵈다 to someone much senior can sound rude.