Seek:
1 to try to find or get something, especially something which is not a physical object:"Are you actively seeking jobs?" she asked.
Hundreds of dissidents are seeking refuge/asylum in the US embassy.
2. To ask for advice, help, approval, permission, etc:
Legal advice should be sought before you take any further action.
search :
To look somewhere carefully in order to find something:
The police searched the woods for the missing boy.
He searched (in/through) his pockets for some change.
FIGURATIVE People who are searching after inner peace sometimes turn to religion.
To try to find the answer to a problem:
Philosophers have searched for centuries but they haven't found the meaning of life.