Seedlings of Cup Plant typically have petiolate leaves. The basal and lower stem leaves of mature plants usually have petioles as well. Those leaves are generally gone by the time the plant flowers, though, so people just notice the perfoliate leaves (the classic cups) that are found on flowering stems. All of the pictures in the database, and Sherry's picture above, appear to be Cup Plant to me.
However, one thing to keep in mind is that Silphiums hybridize freely between species ("promiscuous" is the word botanists like to use). If the person you received the seed from had other species of Silphium growing nearby, like S. integrifolium, it's possible that they collected seeds from Cup Plant, but unknowingly gave you hybrids. That said, I think if you let them grow to flowering size, you'll find that they look like they are supposed to.
