Yes, your peony seems to be blooming with three different flowers. However, even though they appear to be different flowers, your peony may be exhibiting different forms of the same flower.
The Canadian Peony society recognizes five forms of flowers in the herbaceous peony (Paeonia lactiflora)–single, Japanese, anemone, semi-double, and double. See: https://www.peonies.org/flower_types.html. On your plant, some of the flowers seem like semi-doubles and others resemble singles or the anemone/Japanese flower types. There may be a couple of reasons why your plant is exhibiting different forms simultaneously. First of all, some hybrids are apparently of mixed types; as they mature, the flowers can be singles to semi-doubles or semi-doubles to doubles. This is one explanation for the variance in flowers on your plant.
Another possibility is that the ‘less developed’ flowers on your peony are actually the blooms of smaller side buds (lateral buds). Peonies have both large terminal buds and smaller lateral buds. If you remove (disbud) the smaller buds, the main bud on the stem will produce a much larger flower–the plant’s energy is directed into that terminal bud, rather than into multiple flowers. Disbudding is easy to do: “Grasp the area just below the base of the buds you want to remove between your thumbnail and finger and squeeze to pinch the bud off the stem. Pinch off all buds except the one you chose to leave on the stem. Take care not to nick the stem with your thumbnail” .
If your peony hasn’t been fertilized on a regular basis, the plant may not have the energy to produce the fuller flowers on all the buds. Nevertheless, some people may prefer a more floriferous plant and enjoy the variety of flower forms on one plant.
We hope that this will help to solve the mystery of your peony. May your peony prosper.