Yes, there can be a slight band support difference other than it coming with a carrier specific sim card.

For Verizon to T-Mobile, currently sold Verizon iPhone's are all unlocked. That's no problem. Sometimes the sku on the unlocked iPhone is the Sprint sku, though, which can include different LTE band support. The SE is a good example of taking a hard look at which sku you want, as the Verizon/AT&T/T-Mobile model lacks band 7 which is widely used in Europe.
http://www.apple.com/iphone/LTE/

I recall Sprint used to carrier lock their iPhones, AT&T might depending on different plan subsidies. This might be outdated info, though.