First of all, pronounciation of 되 and 돼 is the same:-) 되 and 돼 has the same meaning too. It's a little difficult to explain the meaning of 되 and 돼. It is passive term of "do". Also, I think the closest meaning would be "become", "turn to". I'll explain this with an example. ex. It doesn't work. -> 안돼요. In this sentence, you can't use "되". If you want to differentiate 되 and 돼, you can put 하 and 해 replacing 되 and 돼 and see if it makes sense. ex. 안하요/ 안해요 안해요 is correct and makes sense so in this sentence you have to say 안돼요. Koreans are confused with this grammar too so you'd just have to memorize a few examples to get it right:-) If you don't understand what I said, send a message then I will explain to you!

The pronunciation of 되 and 돼 is not the same. 되 is a monophthong and 돼 is a diphthong. But many Koreans cannot pronounce 되 properly and pronounce it as like 돼. 돼 is a short form of "되어" 철수는 대학생이 됐다. (되었다=>됐다) 철수는 대학생이 돼서 나타났다. (되어서=>돼서) 철수는 대학생이 되고서 사람이 달라졌다. If you replace it with 하 and it will be a correct phrase, it should be 되. If you replace it with 해 and it will be a correct phrase, it should be 돼. 됬다? 됐다? → (핬다 × 했다 ○) → 됐다 되서? 돼서? → (하서 × 해서 ○) → 돼서 되고서? 돼고서? → (하고서 ○ 해고서 ×) → 되고서