To the best of my knowledge, there are no USA jurisdictions that manually count ballots for the first count. Manual counting is only triggered by mandatory recounts, and then limited to just the races affected.
Most central counts have been using optical mark sense scanners, which are those multiple choice test reader thingies. Douglas Jones has posted online an excellent survey and explanation of various election equipment used. http://homepage.cs.uiowa.edu/~jones/voting/
My jurisdiction is very liberal about trying to count every vote marked, per voter intent. I understand that other jurisdictions will reject whole ballots if there's any problems scanning it.
With mark sense equipment, if I ballot doesn't read correctly, it's corrected. Ballots can be unreadable for all sorts of reasons, water damage, unfortunate paper fold, ballot printed askew, etc.
Full image scanner are newer. Votes are inferred using image processing (recognition), vs diodes firing off.
"Electronic adjudication" breaks the paper trail. To correct for voter intent, they're changing records in a database. Versus modifying / correcting ballots or ballot duplication (copying votes to a ballot which will then scan correctly).