Why does shankhini appear in two different groups?

Because the sources split on where it ends. Sent downward it is a channel of elimination; sent to the ear it belongs with the sense channels.

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Secondary channel

Shankhini

Śaṅkhinī · शङ्खिनी

Named for the conch, shankha. It runs down the left of sushumna, between gandhari and saraswati, and ends at the anus in the common list.

conch elimination left side

Side: Left
Ends at: The anus
Carries: Hearing, inner sound and equilibrium
Name means: Conch-shelled, spiral
Variant termination: The left ear, in the sense-organ tables
Associated wind: Apana
Group: One of the eleven secondary nadis
Sources: Shiva Samhita, Gheranda Samhita, later commentaries

Where it runs

Shankhini runs downward on the left of the central channel and terminates in the region governed by apana. In the sources that read it that way it belongs with kuhu and varuni as a channel of elimination rather than of sense.

The minority reading sends it to the left ear, which puts it in the sense group instead. That is the widest kind of variation in the list, and it is worth noticing that nobody in the tradition seems to have found it troubling.

The tables that group the fourteen by sense organ give shankhini the left ear and pair it with pusha or payasvini on the right. That grouping is tidier than the mixed list and is probably later for exactly that reason.

The name

A conch is spiral, and the word carries a ritual charge in Indian religion, being blown to open ceremonies. As a channel name it describes the coil rather than the sound.

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Its wind