Your assumption is correct. This manuscript uses the status "Under review" both for internal and external review. Once the paper was assigned to an editor, he/she conducted an internal review, which is also known as the initial screening. During this time, the status changed to "Under review." Once the initial screening was done, the status changed to "required reviews completed." However, I'm not sure why it changed to "under review" once again. One possibility is that the editor consulted some other editorial board member to decide whether the paper should be desk rejected or sent out for peer review. The status change to "Reviewers assigned" clearly indicates that review invitations have been sent out. Once the required number of reviewers accept the invitation, the status will change to "Under review" once again and the actual peer review process will begin.
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