The title is mostly self-explanatory. Both terms get thrown around a lot. I used to think quantum sensing uses harmonic oscillators / bosons and quantum metrology spins, but this doesn't seem to square with, say, Wikipedia, or this review (arXiv) of quantum sensing.
In particular, the review claims that quantum metrology is "entanglement-enhanced sensing" (and thus a subset of sensing). But then go ahead to define a quantum sensor as a sensor that fulfils (at least) one of the three criteria:
(I) Use of a quantum object to measure a physical quantity (classical or quantum). The quantum object is characterized by quantized energy levels. Specific examples include electronic, magnetic or vibrational states of superconducting or spin qubits, neutral atoms, or trapped ions.
(II) Use of quantum coherence (i.e., wavelike spatial or temporal superposition states) to measure a physical quantity.
(III) Use of quantum entanglement to improve the sensitivity or precision of a measurement, beyond what is possible classically.
(I) is a bit useless, and the distinction between (II) and (III) seems subtle. For example, I would have thought that a cat state fits the moniker "spatial superposition state", but it is also entangled and allows for metrology beyond classical limits. The subclause "beyond what is possible classically" also throws me off, because why talk about quantum sensing when it's within classical limits?
In the next part, they define "Quantum sensors", which logically should coincide with the set of systems that are able to perform quantum sensing, yet their definition does not fit an interferometric phase measurement (send photons in a NOON state into an interferometer to detect a phase).
So perhaps the definitions aren't clearly delineated, or if they are quantum sensing and metrology have finite overlap but neither contains the other?