The word mudra covers three bodies of material that get printed together and are neither the same age nor the same kind of thing. The iconographic layer is a hand position that identifies a figure in sculpture and painting, readable from the early centuries CE onward. The textual layer is the mudras named in the hatha and tantric corpus, where a mudra is a whole bodily technique rather than a hand shape. The third is a twentieth century therapeutic literature of finger positions matched to elements and ailments, which borrows the vocabulary of the other two and is continuous with neither.
Chin Mudra belongs to the second layer. Chin mudra is a textual-layer mudra, named in the hatha material rather than shown on images. It carries the same unresolved problem as Jnana: the sources disagree over whether Chin and Jnana are one seal, two, or the same seal turned over, and the palm-up and palm-down conventions in circulation cannot all be traced to a common original. Which one a teacher uses is a fact about lineage rather than about the text.
The distinction is worth holding onto because the second layer is the one most often collapsed into the third. A gesture named in a hatha or tantric text is attested there in a particular context, usually as one limb of a practice bound to breath, posture and attention. Lifting the hand position out of that context and attaching a health claim to it is what the modern therapeutic literature does, and it is a new claim rather than an old one, whatever the age of the name it travels under.