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The stamp in the passport is placed everytime you enter the country no matter which passport you carry.
There used to be a relaxation in this rule for US citizens travelling to & from Canada, but this has changed since middle of 2000, and it is required that you carry your passport at all times.
There are some facilities for regular travellers with the use of INS TransPass, an ATM-like machine located at some POE, and land border crossings. Anybody can get this, including non-US citizens, but there are some rules that have to be satisfied by everybody (# of days of travel, type of work, etc.)