iPhone 7 never shows "LTE" even on LTE network

I have an iPhone 7 which I bought directly from Apple, and my SIM contract is with Three here in the UK. I have been using this phone happily since September, I had noticed the mobile data connection flips between *3G* and *4G* which I thought little of at first. I figured 3G = HSPA/+ and 4G = LTE. However, the other week I was with a friend in the US who had recently got a 7 plus. She is with AT&T and I noticed that her phone was most often displaying *LTE* as the connection type. I thought this was odd as I had never seen this on my own iPhone 7 and had presumed that 4G meant LTE. I did a little googling and found some discussions which claimed that on iOS the 4G mean HSPA+ and 3G means regular old 3G. In this case I was double confused as my carrier, Three, supposedly has a 4G LTE network and so I should see LTE from time to time. I understand that Three does not have an LTE-Advanced network, only regular LTE. So is this perhaps the distinction and confusion? 4G = LTE and LTE = LTE-Advanced? Could somebody perhaps clear up what is going on? Do I need to contact my carrier to change the network connection settings on my phone? If I can make use of the iPhone 7's faster mobile data tech then I would like to as I am a very heavy data user. The reason I went with Three was for their unlimited data tariff. EDIT: As requested by owlswipe. A photo showing Speedtest saying the network is "Three LTE" with the network icon at the top left saying "4G" which it did throughout the test. I am on 40th floor of a tower here so speeds aren't fantastic...