I look for a car (any car)
I search for a car (a specific car; I know which one it is, you probably don't)
I search for the car (that I mentioned earlier, and thus you know of it now too)Maybe this is done by some change in congruence on the verb - maybe all specific-or-definite verbs have a certain marking, while only definite nouns have a marking, or vice versa. Or maybe only certain verbs where the distinction is felt to be significant enough have pairs where the difference is meaningful. I would imagine the pairs would tend to look similar but not have any regular formation going on.