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unique column constraint vs unique index
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Yes, they are the same.  A unique constraint in a table definition is exactly and precisely the same as an explicit unique index, save for what is different:

 - an explicit UNIQUE index may contain expressions, a UNIQUE constraint in a table may only contain bare columns  
 - you have control over the identifier name of an explicit UNIQUE index but have no control over the identifier name of a unique index created by a unique constraint  
 - you may drop or create an explicit UNIQUE index but you may not explicitly drop or create the index implicitly created by a UNIQUE constraint