PMBOK says, "The key benefit of Plan Communication Management is that it identifies and documents the approach to communicate most effectively and efficiently with stakeholders."
So Communication Management Plan should be input to Stakeholder Management Plan.
Manage Stakeholder Engagement should concentrate on engaging stakeholders in the project, handling conflicts, dealing etc.
PMBOK should reassess their standards Saving Changes...
In case you weren't already aware of this, the two knowledge areas used to be a single one and even when they were separated as part of the Sixth (?) edition, there is still a significant degree of integration and overlap between them.
I would also suggest that one can't complete a Communication Management Plan until one has a good understanding of one's stakeholders - more than just identifying them. As such, there are elements of each plan which could be considered inputs of the other, and this underscores the iterative rather than linear nature in which these artifacts get developed.
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