The Twin Sisters nomenclature is difficult.
Looking at the
topo, "Twin Sisters Peaks" is written near the 2 northern summits, Pt's 11428 and 11413, often referred to as the east and west summits. The west summit is unranked.
"Twin Sisters Mountain" is kind of sprawled across the whole area above treeline, including the three 11er summits and a couple unranked 10er points. Roach's list (and now John's) have called Pt 11376, the southern ranked 11er, Twin Sisters Mountain.
My interpretation is that TSPeaks refers to the 2 northern summits specifically, while TSMountain refers to the larger mountain in general. I think ranked Pt 11376 is probably unnamed.
If you type TSPeaks and TSMountain into topozone, both give an elevation of 11428. The location is a little different, TSP going to 11428 while TSM goes to the saddle between the 2 ranked summits.
Totally clear, right?