I have clematis with small white flowers growing wild on my property, and since I have lots of invasives (oriental bittersweet, buckthorn, Berberis AKA barberry, etc) I was worried that I had C. terniflora. So I did some research as to how to differentiate. The easiest way for me is that the leaves look quite different.
Here's a link to C. viriginiana:
http://www.carolinanature.com/...
Leaves are 3 parts with large-toothed edges
Here's C. terniflora:
http://www.finegardening.com/s...
Leaves also have 3 parts, but are more rounded with smooth (botanists call this entire) edges.
