In fact,the meanings between two are sometimes overlapped.
寻找 can be used as looking for something. Looking for you wallet,keys,etc.
Looking for you wallet-->寻找你的钱包
You can use 寻找 as "find".
Finding a partner-->寻找一个伙伴.
Finding inspiration.-->寻找灵感
搜索 is mostly used as searching.
For example:Searching the keyword-->搜索关键字
Or,searching for a missing man.-->搜索失踪的人