meaning of phrases

Certainly, there are register differences with the former being more formal, more momentous and the latter more conversational.

Have you gotten yourself a Longman Language Activator yet, Ms Tan. You'd love it!

You look for your car keys. You go in search of the Lost City of Gold, or a complete fossil of T. Rex. One is "now which pair of pants did I leave them in, or oh my god are they still in the front door lock where anybody can just walk off with them?" The other is "Let's see, I need a half-dozen moving vans, sixteen 6-man tents, three tons of dynamite, a hundred and ten shovels, and a squad of marines, and we'll have to charter a freighter to get there." I suspect that's what JTT means by momentous.

Well, "in search of" is a phrase without a verb, and to "look for" is a phrasal verb. That's one difference. "To be in search" of something is a rather bookish phrase often used to denote a quest extending over time, whose outcome is expected to be somewhat deferred or uncertain, e.g. for a cure, for happiness, enlightenment, vindication, "closure" (US), etc. Thus to write or say "I am in search of my pen" without jocular intent could be heard or read as ponderous and excessively formal. German tourists might say "I am in search of Buckingham Palace". "I am looking for" would be better because the matter is simply resolved by looking at a map or asking somebody.

To search for something implies a more thorough and active endeavour than merely looking for something. A searching examination is one that is thorough and painstaking.

Preterxactly, MJ. Well done and a tip of the hat to Contrex as well.