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Is there are difference between these words?

hi

1) 두뇌 and 뇌
Both are almost same. But a tiny diff can be in situation.
두뇌 is used typically with meaning of "BRAIN"
뇌 is used in medicine...
Anyhow two words is same.
2) 개발 and 발전
개발 means making something. ex: Developing program...
발전 means growth of something.
I hope this is helpful for you... Good luck

First question was well explained by apollo-sun.
Here are some examples for better understading.

개발 contains meanig of fix and make it better.
The construction company started the project for developing the city.
The man developed his computer skill.

발전 contains meanig of stages such as level 1, level2, level 3... .
Step by step, the nation developed their economy .