Hi Laurie. Good observation. It depends on your take on the verbiage, but in my books Itoh refers to a plant produced by a lactiflora x woody peony cross whereas intersectional is a broader term that involves a group other than the lactifloras being crossed with a woody peony (herbaceous hybrid e.g. Lemon Chiffon x woody peony).
Peony 'Eurasia' (not registered) would be an example of an intersectional but NOT an Itoh which was produced by P. officinalis x P. rockii. A crazy cross!
Herbaceous hybrids are herbaceous plants that have more than one species in their ancestry.
Itohs do indeed form axillary buds which is a product of their woody peony ancestry. In growing zones warmer than mine these buds can overwinter and produce growth. I have seen this once on a herbaceous hybrid, but think it was a weird chance occurrence. I have never seen it otherwise.
Interestingly enough, axillary buds on Itohs can be used to propagate them through micropropagation. Bob Johnson has said that when he was working at Caprice Nursery they would see rooting from stems and resulting growth from these buds when they cut the stems up and wrapped them in damp paper towel or newspaper.
