Every Petal Sets a Seed
In a true sunflower (Helianthus), the showy outer "petals" are ray florets that are sterile — they advertise the flower but set no seed, and all the seed forms in the central disk. False sunflower works differently: its ray florets are fertile. Each ray produces a seed, so the outer rim of every head sets seed alongside the disk. This is one of the clearest technical features separating Heliopsis from Helianthus, even though the two look much alike.
A second tell follows from it: the rays of false sunflower tend to persist rather than drop. As the head matures they stay attached, fading to a papery cream rather than falling away, so a ripening false sunflower keeps its star shape long after a true sunflower would have shed its petals. If the rays are still there as the seeds fill, you are almost certainly looking at Heliopsis.