They may be NPS properties, but they are not formal 'National Parks'.
No legal difference. If it is owned by NPS, then the rules that apply in named National Parks very nearly always apply (I know, having professionally dealt with NPS a lot).
For example, should the 'Blue Ridge Parkway' be redesignated as 'Blue Ridge National Park', then of course the list would change.
Local anti-auto activists and NIMBYs in the Washington area have repeatedly renamed Rock Creek Park in the District of Columbia to Rock Creek
National Park. No difference (the park does extend north of D.C. for many miles as Rock Creek Park, owned not by NPS, but by the Maryland-National Capital Park and Planning Commission).
The National Mall and the monuments and memorials along it are all under NPS ownership, and are
very definitely considered national parks.