Endless discussions can be had about what species are. And as you may know, there are ‘splitters’ and ‘lumpers’. Biological (do they cross easily), morphological (do they look alike) and genetic (how different is the DNA) definitions are possible and even there you have the question of how much difference is needed to have another species or subspecies or form etcetera. I personally think that Donald Smith has made a very good summary of the peony species, it’s available from the American Peony Society as it was published in their Bulletin (last year I think). He takes both morphological and genetic data and was able to merge both into one classification. Some of the ‘new’ species are missing, but I think ‘hard to improve upon’.

Garden varieties are rarely pure species. Mostly they are from open pollinated seeds collected in other (botanic) gardens where many species grow and they tend to cross-pollinate often so most are ‘garden hybrids’. One has to look for the defining characteristics and the origin. The best would be a representative specimen of the species grown from wild collected seeds. That is actually rather rare…

That being said, I think your delavayi has very attractive uncommonly narrow leaflets :-)