The counter there and the one for the badges are two independent concepts.
Strunk & White and Copy Editor can be earned by suggested edits. But they can also be earned by the normal edits you can perform on Community Wiki posts, or on any post when you hit 2000 reputation. Furthermore, the rejected edits don't count as edits because they are not committed into the system.
So, the number of
approved suggested edits does contribute to getting those badges, but it is not necessarily the complete picture. It is also not necessarily accurate that all of those listed would count, as the badges don't care about tag-only edits. Suggested edits may include those which are tag only.