What does "awaiting reviewer reply" mean? Is it same as "under review" and "awaiting reviewer scores"?"
closed as off-topic by user3209815, Buzz, Scientist, scaaahu, gman Aug 30 '18 at 14:55
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It means reviewers have been invited but have not responded to the invitation.
It's not necessarily the same as 'under review' and 'awaiting reviewer scores'. The latter is a clear term that means reviewers have agreed to review the article, but have not provided a report yet. The former is a vague term that could mean anything: reviewer has been invited, reviewer has agreed to review, maybe even reviewer has submitted a review but there're other reviewers who have not yet completed their reviews.
In any case, there's nothing to do except wait.
For your purposes as an author, I would recommend regarding it as effectively the same. There are a lot of different journal reviewing systems out there, and they use varying (and sometimes unclear) language. I thus recommend against trying to parse the language too carefully. What's clear here is that the peer review process is in progress and you can't really do anything but wait, whatever nuance the system might be telling you about the ongoing interactions between handling editor and reviewers.
You may also find this description of a typical journal workflow useful in helping to understand the major stages and decision points.