I have heard that in USA people usually present gift along with its receipt from store to allow one to return the gift to the store?
Gift receipts have come into fashion in the last couple of decades. Some stores allow returns of items that they carry without receipts, but often only for store credit. Others require receipts for any return. Gift receipts are a recognition the consumer reality of gift giving and they allow the giver to spend an amount that they are comfortable with, show that some thought and time was spent choosing something that they think the receiver will like, but acknowledging that the receiver may for one reason or another prefer something different.
Gift receipts are also often given for wedding gifts or birthday parties where the recipient may receive many gifts, and duplicates of certain items.
Some people still feel that it would be poor taste to return a gift that someone has given, and some give "gift cards" that grant credit at one or more stores or prepaid credit cards that allow money to be spent with any merchant that accepts those cards from the affiliated network for payment.
There is no definite answer about whether a gift receipt should be included with a gift given, but it is culturally acceptable to give them, and it is common for them to be given with clothing purchases.
It should be noted that "gift receipts" are printed separately, and serve as proof of purchase without saying what the purchase price was (since, like leaving the price sticker on the gift, that's considered bad form; people should value the gift for itself, rather than by its price.)
Also, gift receipts are much more common, and much more valuable, for items like clothing where the issue may be that the fit isn't quite right and an exchange would be appropriate, rather than it being entirely the wrong object.
Finally, many manufacturers make warranty service much easier to obtain if you have a receipt showing that it was purchased new rather than used and the date on which it was purchased, and the gift receipt (again, preferably without the purchase price) can be used for that too.
As far as the ettiquette of exchanges goes: Exchanging something to fix a minor detail like size or color or "oops, the zipper wasn't sewn in properly on this one" is simply a realistic response to the problems of buying mass-produced goods for someone else. Exchanging something to replace it with something similar but different is a trifle declasse'. Exchanging it to buy something ENTIRELY different starts to become statement that you didn't appreciate the effort someone went to in order to select the gift -- you hate it or them or both. Unless you're really on the edge financially, I think Miss Manners would say "if you really don't want it in the house, give it to charity or regift it rather than returning it." Among other things, returns are a pain in the posterior for store owners, and really shouldn't be used as a substitute for "I was too embarrassed to just give you cash."