Blue Ridge Parkway
Peaks of Otter are National Park Service lands, however it is surrounded by Jefferson National Forest. I have never found a really good map of the dividing lines. I have hiked in the area and been told I was in the National Forest sometime and not even having gone far, but in another spot I went a long way and never left the National Park.
Yes, the Peaks of Otter is National Park Service (NPS) lands, and part of the Blue Ridge Parkway, which is mostly a narrow easement that runs the length of the parkway, from Afton Mtn in Virginia, over 400 miles south to Ashville, NC. Periodically, the parkway NPS lands broadens to include additional recreational areas, such as the scenic Peaks of Otter. Most of the trails around the peaks are within NPS boundaries.
If you really want to get an idea of the boundaries between national park and national forest, you will need to get a USGS topo map. The boundaries are well marked on the topo maps, and typically, the park service maintains good boundary markings along their property lines.
Hope that helps..