hand me that pair of pants, implies there is only one pair of pants from which to choose. If I looked in a bin of user interface elements and there was only one control then I could just say
hand me that control.
But when there are 11 pairs of pants on a table, how do you ask?
Hand me a pair of pants? Will any pair of pants really do? Are you going to a wedding? A rodeo? An awkward office party? I posit in that scenario you would either ask your question and not get what you wanted, or you would ask
Hand me the tuxedo pants or
Hand me the jeans or
hand me those awful khakis.