Hm, I think you have it mostly right. Spot (and Listen) are mostly passive tests of your visual (or auditory) accuracy and attentiveness. Search, on the other hand, is actively poking and prodding in an area to find something. Search, therefore, could trigger a trap, but Spot would not. Search would also take time, while Spot would be mostly instantaneous.
You could use Spot for Search only if the DM decides that the item in question is "hiding in plain sight", or very inexpertly hidden. You could use Search for Spot only if you had the luxury of poking around in the bushes or in closets for an ambush.
By the way, I bring up Listen because the difference between Spot and Listen is intuitively clear to me, although others might disagree. Spot is used for something that could be seen; Listen is for something that makes a noise.
If I were DM I'd either give two chances or use the higher of the two in many circumstances. Sometimes, though, I might rule that the character can only Spot (e.g. a magically silenced assassin, or too much loud noise), or only Listen (e.g. an invisible assassin, or something sneaking up right behind him, or pitch dark, or blinding light, or the character is explicitly watching only in one direction). Someone who chooses to be keen-eyed (or sharp-eared) might end up disadvantaged if the other sense is required ... but such is life.
But, all that aside, I can imagine a character with sharp eyes who doesn't really know how to search, or a fairly average bloke who's trained to think deviously when searching. So in this case the two skills can be justified.
"On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question."
- Charles Babbage (1791 - 1871)
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