They're synonyms. :) But "seek" doesn't tend to be used in informal speech very much...

"I'm seeking my soul mate." "We are searching for the missing person." " I'm looking for my keys but can't find them anywhere!" Hope these examples help make the differences in usage a bit clearer!

'seek' means try to get or reach, which needs an effort or attempt, 'search' means looking thoroughly to find the answer, ' look for' has the similar meaning with 'find', but the former one means the finding process( haven't find sth.) If you have other questions, you can ask me. I'm glad to help;)