iPhone 5 introduced LTE. iPhone 5S has LTE as well. I have T-Mobile, and also occasionally run into 4G, instead of LTE. However this only happens when I'm in area are that barely has service. If I see the 4G icon, I know I'm close to an area that could have no service. For me, this is consistent with certain large warehouses, basement of building, etc.
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I just remembered about a year or so ago that I had some trouble with my original IP5 S and took it into the Genius Bar. They made me a deal where I paid around $200 and they gave me a replacement. In "about", it does say it is a NE298LL/A model which I see on the internet means it might be a TMobile model. I don't really care one way or the other since it does work as it is our home backup and I'll soon be getting the new IP8 and this phone will be going back into the drawer. I just thought it was strange to see 4G come up when I'm not on wifi.