You are comparing two different things here AFAICT.
5G is a cell phone standard, and the dedicated frequency range you are referring to is used by something like the (LTE-based) FirstNet.
TETRA is a non-phone based protocol, and it is more comparable to the Public 25 radio system.
5G is set to replace tetra, with dedicated frequencies for emergency services, and those features implemented - so this will become the "mobile phone", using dedicated frequencies on current basestations, while the data in the backend will be transfered via 5G standards (with additional moficiations for PTT and group talk).
So yes, the technology behind is different, but the usecase will be the same.