Agree that it is a Clematis. Are the flowers fragrant and do you have a pic of it in bloom?

It is clematis, and there are several that bloom with small white flowers late summer. You could post this on the Clematis forum along with any photos you have of the flowers and more mature foliage to try and get an ID. It may be C. terniflora, sweet autumn clematis, but the leaves can look a bit different early in the season, so it may be something else.

Silver lace is the common name for Fallopia baldschuanica, a completely different vine from a clematis.

As Babs notes, there several different late blooming clematis with similar looking flowers but this looks very much like sweet autumn clematis. C. terniflora. This is considered an invasive species in some areas. If the leaves retain the entire leaf margin as the plant matures - no teeth or serrated edges - then SAC is what it is.

After looking at some photos online from Spring Hill Nursery, it is the SAC. Thank you all for the help.

There are other clematis that have similar small white flowers. I've seen at least 3 others, and the only way to easily tell the difference is the leaves. While your highest chance is sweet autumn, it really isn't the only one IME. As GG48 said, if it turns out to be SA, it is invasive in many parts of the country, so trim it back before it goes to seed if you are in an area where the seeds have time to ripen, or you will find it reseeding all over your yard, the neighbors' yards and any nearby woods.

Yes this generally similar clematis species will be told apart from one another by specific details of their structures and their behaviors (such as when they bloom).

The plant I have has not been invasive at all. It remains in the same place where originally planted with the same root base size from 6 years ago. I cut it back every year simply to remove the dead leaves and vines from the fence. It blooms every year in mid-August and the flowers really do not give off much if any of a fragrance. In my opinion it isn't invasive, does that mean it isn't the SAC? My local nursery carries the SAC and I was hoping to get new ones planted.

You would be unlikely to see any invasive tendencies. These generally don't show up as seedlings in the garden (although they can) but typically the wind and birds distribute the seeds over a large distance. If appearing in a neighbor's garden, it might well get weeded out but in a natural area, it will grow unchallenged. It is also not considered invasive in all locations (not at all here in the PNW).

All of the three species that bloom with clusters of small white flowers in late summer/early fall - Clematis terniflora, C. virginiana or C. vitalba - have mildly honey or hawthorn scented flowers. Not a strong scent but present.

Are you somewhere relatively warm, like zone 6 (-10 degrees as coldest winter temps.) or warmer? SA isn't invasive as far as roots spreading, but it does seed around rampantly in many places if the seeds have a chance to ripen. I am not sure if you would have noticed after only 6 years since the seedlings would have to get large enough and prolific enough to be noticed. Around here, frost hits too soon after bloom for seeds to have a chance to ripen, so it isn't an issue at all here.

I have C. virginiana that occurs here naturally, but its leaves have teeth, unlike yours. I've also seen one in the desert SW that was far enough from civilization so I am fairly certain that it was native, and though I researched it at the time, I don't recall what I decided it was.

I live in western Colorado. Fairly mild winters here in the valley. Thank you all again for the helpful information.