These conditions, whilst both referencing "myalgia" which means "muscle pain", are not the same. Whilst certain aspects of these conditions are similar, they have different origins.
It is believed that Polymyalgia is an autoimmune disease with muscle inflammation, muscle stiffness, pain and weakness being its features. Fibromyalgia is not an inflammatory condition but is originated in the nervous system's processing of bodily sensations. Tiredness, headaches, over-sensitivity to touch can be its features as well as pain in multiple areas in the body.
Pilates can help with both and is especially good for fibromyalgia. For polymyalgia, gentle exercise alongside the prescribed anti-inflammatory medications can be very useful. We need to be careful to work within your current physical limits, be mindful of your body's responses and stop when needed.