From my point of view the term "total solution authored" means, that you provided a solution to any other user.
"Total solutions marked accepted" means for me, that you accepted posts of other users as solutions to your problems.
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How to Get the Most from Your Signature in the Community
Makes sense. Perfect!
[EDIT] and also I could see the Total Solutions Marked Accepted incremented by +1 after I marked your post as solution!