These two verbs are usually confused. However, they have different meanings. Have a look:
When we use the word SEARCH without a preposition, it means we are talking about the area we are looking.
Examples:
I searched the ocean (I swam around in the ocean and went on a boat looking for something).
He searched his car all day long but never found it (He was looking in his car – in the trunk, in the seats, etc – for something)
When we use the preposition FOR after SEARCH, it means we are talking about the actual thing we want to find.
Examples:
I searched for my keys and couldn’t find them (I didn’t know where my keys were so I looked around my apartment for them).
He searched for his car (He had forgotten where he had parked it and was looking to find the automobile).
We can also have two objects after the word search. We first say where we are looking, and then what we are looking for (following the word FOR).
Examples:
I searched my apartment for my keys.
He searched the city for his car.
(Source: https://www.englishwithnick.de/online-english-lessons/search-and-search-for-difference/)