My phone had been stuck on "4G" for days. Repeated airplane mode toggles didn't restore LTE but on a whim I power cycled it. LTE is back.
The bugs run deep.
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4G vs. LTE is a display choice in the OS with the carrier choosing which one to use.
Airplane mode disables cellular radio transmit/receive. It typically doesn't turn it off.
Current Snapdragon basebands include cellular, Wi-Fi and Bluetooth via separate sandboxed processes.