IMO, "2-way checkback" is a synonym for "2-way NMF", but "2-way NMF" is a misnomer (since it's not only "new minor" forcing any more, it's both minors) & shouldn't be used (even though it's on the ACBL card that way).
As for the distinction between 2♣ forcing 2♦ or not, that's the difference between "2-way puppet checkback" vs. "2-way checkback"

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