Yes, that's one way to differentiate them. Even the buildings are very different. The liberal United Church of Christ usually has majestic, soaring cathedral-like structures. Most of the church of Christ buildings are very modest and quite a few don't even have steeples or other such ornamentation. I could also mention the difference in the music...but that's left as an exercise for the reader. :-)
I'll share this story (which I've posted on occasion here on Free Republic). Back in the summer of 2008 when the campaign was in full swing, I took a long summer vacation by car. My route took me across Texas, into Arkansas, through Missouri, Illinois and Tennessee as well as Alabama. I visited congregations of the "coC" at every opportunity for Wednesday night as well as Sunday services. I checked out the parking lot of each. There was NOT ONE Obama bumper sticker on any of the thousands of cars I must have seen. There were plenty for Palin (with the name of some other guy, the fellow she ran with).
In closing, since I'll heading to services in a few hours, everyone at my congregation is a gun owner and that includes the preacher. Woe unto the fool who tries to lift the collection plate. We carry more than just our Bibles into the building! Amen!
The mixing up of our beliefs and actions with that den of depravity and anti-Americanism in Chicago is unfortunate.