If Stellacorn is in a draw and survives but is the attacker, and gets pushed back to base, does it count as a move and draw one? Same question for something like Eye of the Herald.

No, your Stellacorn Herder will not draw a card in that scenario.

According to Rule 450 and established RiftJudge FAQs (specifically FAQ #10124, FAQ #10165, and FAQ #10159), a Recall (the process of moving a unit back to the base after it is stunned or fails to conquer) is strictly defined as a game action distinct from a Move.

Because Stellacorn Herder's ability ("When I move, draw 1") specifically triggers only upon a Move action, it does not trigger when the unit is returned to the base via a recall.

Summary:

• Recall vs. Move: The game rules define these as separate actions. Being recalled to the base following combat (even in a "no result" or tie scenario) is a Recall (Rule 450), not a Move (Rule 144).
• Result: The ability does not activate, and you do not draw a card.

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