Difference between wing chair and armchair
Solution 1:
A wing chair has 'wings' up the side, originally intended to shield the sitter's torso and head from drafts. In these days of central heating the wings are just a 'design element'.
Solution 2:
I've never head of a "wing chair". I think that might be more technical term, that you would use in a furniture store, but nowhere else.
"Armchair" is much more common.