Let's see what can be sought:
love, employment, advice, support, fame, happiness, revenge, permission, refuge, fortune, enemy, peace, knowledge...
and what isn't usually sought but is looked for:
a pen, blouse, book, chair, house...
I have a feeling people would rather seek things that are intangible, non-physical.
Seek applies to things that, despite being out of sight, seem to be near at hand and should be easy to find.
Search implies the difficulty of the pursuit because what you search for is probably remote or hidden or both. You search by seeking in many places; seeking suggests going to the place where the object is supposed to be.