Note use of the defined terms “X” and “Y” in the following, from the 2002 ISDA master agreement (discussed in this post):
If a party is so required to deduct or withhold, then that party (“X”) will:—
(1) promptly notify the other party (“Y”) of such requirement;
(2) pay to the relevant authorities the full amount required to be deducted or withheld (including the full amount required to be deducted or withheld from any additional amount paid by X to Y under this Section 2(d)) promptly upon the earlier of determining that such deduction or withholding is required or receiving notice that such amount has been assessed against Y;
(3) promptly forward to Y an official receipt (or a certified copy), or other documentation reasonably acceptable to Y, evidencing such payment to such authorities; and
(4) if such Tax is an Indemnifiable Tax, pay to Y, in addition to the payment to which Y is otherwise entitled under this Agreement, such additional amount as is necessary to ensure that the net amount actually received by Y (free and clear of Indemnifiable Taxes, whether assessed against X or Y) will equal the full amount Y would have received had no such deduction or withholding been required.
Using “X” and “Y” is one way to handle the awkwardness that can arise when you refer to the parties in describing a procedure in which either party could play a given role. You could use “that party” and “the other party,” but that doesn’t work if you need to refer to “that party” after having referred to “the other party”—the reader could think “that party” refers to “the other party.”
But “X” and “Y” are devoid of any context, so you force the reader to remember what hats X and Y wear. The same applies to using instead “the first party” and “the second party.”
So I’d be inclined to use instead, in the ISDA master agreement, “the deducting or withholding party” and “the other party.” Sure, instead of “X” you’re using five words, but you’d use them only three times in the quoted extract, so I think it’s a price worth paying.
And outside of this example, more likely than not you wouldn’t have alternative designations for a given party, so you could more economically say, for example, “the purchasing party.”