search is going to be slightly more efficient than where, but not enough that you would notice for any realistic search scenario. Both commands can comparing the value of a field to some static value, but that is where the commonality ends. 'where' can be used to compare 2 fields against each other, to compared complex functions of a field to other fields or static values. E.g. you can't do something like to compare fields x and y.
| search x>y
That search would actually search for cases where field x is greater (lexicographically) than the literal value "y"
Note that this is also why the syntax for search and where are slightly different. Because search is designed to compare a field against a static value, it assumes the right hand side of any expression is a literal value. For where, the RHS can be a literal or a field, so literals need to be disambiguated by using double quotes.
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