Long time ago, I wrote mass spectroscopy, by mistake, in an undergraduate exam and the instructor told me "You were the only one in my class who wrote mass spectroscopy." The explanation was that MS is mass spectrometry because it does not deal with light or electromagnetic radiation and that's what the textbook said. At that time internet was not that common. Now I searched the term "mass spectroscopy" in papers using Google Scholar and there are 1,100,000 results with this exact phrase. There are 2,330,000 results for mass spectrometry.
It seems, given the usage, and the difference is not that strict. Consulting the controller of all chemical terminologies, IUPAC says
The study of physical systems by the electromagnetic radiation with
which they interact or that thay [spelling mistake] produce. Spectrometry is the
measurement of such radiations as a means of obtaining information
about the systems and their components. In certain types of optical
spectroscopy, the radiation originates from an external source and is
modified by the system, whereas in other types, the radiation
originates within the system itself.
You will see famous books, especially by Griffiths with the title "Fourier Transform Infrared Spectrometry" and nobody raised an eyebrow.