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Spectroscopy is the study of spectra, spectrography is the writing of the spectra, and spectrometry is the measure of spectra. So from an etymological perspective, there is no real difference between the three. On arXiv, there is for instance an article that uses the term "spectrometry" in the title, but "spectroscopy" in the abstract (several, actually) to designate what seems to be the same thing.

But perhaps are there differences between the use of these terms in astrophysics?

There are certain techniques that are designated with one term rather than the other (e.g I haven't seen any mass spectroscopy, but have seen mass spectrometry), but is there a conceptual difference between spectroscopy and spectrometry?

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    $\begingroup$ Ha! I was going to leave a comment suggesting that you read the tag definitions but one doesn't have one and the other is pretty lame! I think I know the difference between a spectrometer, a spectroscope and a spectrophotometer, and between astronomy and astrometry, but yikes this one could use an authoritative answer and then some better tag definitions. $\endgroup$ – uhoh Dec 19 '19 at 15:32
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    $\begingroup$ @uhoh Actually, my question comes from looking at the tag definitions. I was surprised that both tags weren't synonyms, since I often use the two terms interchangeably. But I figured there must be a good reason, i.e the two don't actually mean the same thing. $\endgroup$ – usernumber Dec 20 '19 at 7:54
  • $\begingroup$ Main practical difference is that spectroscopy physically scans an electromagnetic spectrum and spectrometry usually refers to masses or property related to it as kinetic energy at given condition. But the terms used interchangeably don't really confuse the reader, context given. Normally, anyway, spectrometry is spectrometry of mass while spectroscopy is everything using em radiation to pump and/or probe a sample. $\endgroup$ – Alchimista Dec 20 '19 at 9:06

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