chercher is a transitive verb whereas fouiller can be used transitively or intransitively
chercher means to look for (Je cherche mes clés. - I'm looking for my keys).
chercher can also mean to look up (such as to look up something in a dictionary)
fouiller when used transitively means to search (as in when a security guard searches you to determine if you have a concealed weapon).
fouiller can also mean to rummage when used intransitively
so consider these two sentences
Il a fouillé dans mon sac - He searched my bag (the security guard searched my bag to see if there was anything untoward hidden in it)
j'ai cherché mon sac - I searched for my bag (which I had mislaid)