Those expressions are having some meaning of 'if' but a bit different. Let me tell you by using an example. 만났다면: ex) 내가 그를 만났다면 = This is having both "If I met you " and "If only I had met him" 만났더라면: ex) 내가 그를 만났더라면 = this expression has only the meaning of "If only I had met (but I didn't meet)" I hope my comment to be able to help you^^

In terms of grammar, "만난다면" is for the zero, first, second conditional, on the other hand, "만났더라면" is for third conditional. e.g. When(or If) I meet him, I will tell him I love him = 내가 그 사람을 만난다면, If I met him, I would... = 내가 그 사람을 만난다면, If I had met him, I would have told.... = 내가 그 사람을 만났더라면, \^o^/

-다면 can be used with any tense. -더라면 can be used with past tense only and used for supposing something which was not happened. ex) 내가 너처럼 건강하다면 좋겠다. 만일 어제 서울에 눈이 왔다면 길이 막혀 고생을 했겠다. 네가 그 꼴을 보았다면 아마 기절했을 것이다. 아이가 동전을 삼켰다면 큰일이다. 너도 그 사람을 만났더라면 좋았을 텐데. 조금만 더 노력했더라면 성공했을 거야. 그때 네가 안 왔더라면 큰일 날 뻔했다.