The styles of "pure" R. palustris are fused and do not protrude from the hypanthium (very similar to the styles of Rosa rugosa or Rosa bracteata).

The styles of R. palustris plena are protruding (similar to those of Rosa multiflora or Rosa arvensis).

To me, Rosa palustris plena is probably an old hybrid, rather than a multi-petaled sport, especially since stamens are often converted to petals in those instances.

The English Flora: Or, A Catalogue of Trees, Shrubs, Plants and Fruits, etc. p. 36 (1775)
By Richard Weston
45. Double Pensylvanian Rose - pensylvanica plena. 61.
61 pensylvanica plena - Double Pensylvanian Rose

Catalogue of Fruit and Ornamental Trees and Plants &c. Cultivated at the Linnaean Botanic Garden. 21st Edition, 1822 p. 30
By William Prince
64 Double Pennsylvania, autumn flowering, very delicate, 50 cts.