How come when I click "Improve" on an edit suggestion the approval is passed on to the Community user?
The approval is shown as coming from Community as a means of quickly identifying that it was an "Improve" action rather than a standard "Approve" action. This has slightly less of an impact here, since only one approver is necessary. Elsewhere, it's basically "Community is approving the edit so that you can step in yourself", which I see J.M. illustrated nicely in the comments above.
However, it remains useful because this makes it an explicit scenario to track. By having the approver be Community, one can instantly observe what edits are getting Improved, rather than what is getting straight-up Approved.
The person responsible for the Improve action is also readily available, as it will always be the user whose edit comes immediately after the Improved Suggested Edit.