The function of a Pyrometer is the same, correct.
However the term Pyrometer when searching on the Internet will bring back results for all manner of temperature measurement devices that are not a modern Thermopile based IR Thermometer. It's a little like searching for an "internal combustion engine" when all you are really only interested in is the Diesel engine !

Pyrometer is an over arching category of test equipment that merely details that it is a thermal radiation measurement device.
Fraser