寻找--you can do it by your eyes
搜索--you have to use your hands, because the thing you want to find out is concealed by other things.
If I hide some money in my house and you want to find it out, you probably have to use your hands to open boxes, drawers, put vases up side down, move some furniture a little bit.....you can't just do it with your eyes. In this case, use 搜索
Another way to use 搜索, is like a group of people(police, investigators,) searching for clues, bodies, fugitives, missing child....