The two products may be identical, but they are not the same
One of the sneaky tricks pulled by salespeople is the “We match any competitor’s price on the same item” offer. The trick is to make sure the products in your store are not available at any competitor by simply changing the model number.
I read that this trick is particularly popular for some reason with furniture stores (in cahoots with furniture manufacturers). They will sell you a Fabrikam model 1310-XD-2 sofa. You spot the same sofa at a competitor and they say, “No, it is not the same sofa. That sofa is a Fabrikam model 1310-XC-2. The one you bought is a model 1310-XD-2. Sorry.”
The two sofas are completely identical in every respect of any consequence. The only difference is that the furniture manufacturer prints 1310-XC-2 on the tag of the sofa it sells to store A and 1310-XD-2 on the tag of the sofa it sells to store B.
Since the model numbers don’t match, the price match guarantee does not apply.