If you buy an iPhone from Target, they sell SIM Free iPhones, not the carrier specific model. But these SIM free iPhones are subject to the US Reseller Flex Policy. What this means is that when you initially activate them, whatever carrier's SIM card is in the device is the locking policy that gets attached to the IMEI of the device (and any warranty replacement device that you get in the future).
So, if you were to upgrade a Verizon line through Target and then put an AT&T SIM in the phone for the initial activation, it would become locked to AT&T. Conversely, if you were to upgrade an AT&T line through Target, and put a Verizon SIM in the device for the initial activation, the device would be unlocked since all Verizon iPhone are unlocked.
So, if you were to upgrade a Verizon line through Target and then put an AT&T SIM in the phone for the initial activation, it would become locked to AT&T. Conversely, if you were to upgrade an AT&T line through Target, and put a Verizon SIM in the device for the initial activation, the device would be unlocked since all Verizon iPhone are unlocked.