I have upgraded on both my iMac and Macbook to LR Classic. But LR CC still exists on both. So when I turn on either computer, both versions still show up. Should I uninstall the old one? I thought it automatically updated CC to Classic and removed the other when I did the update, but that did not happen. Thanks for any advice!
That depends on the exact version and name of the software.
If it is Lightroom CC 2015, version number 2015.X (where x is some number), you can uninstall it, as all features of this software is included in Lightroom Classic CC (plus some new features as well).
If it is the very new Lightroom CC, version number 1.X, this is brand new software that didn't exist before October 2017, which stores your photos in "the cloud", automatically, you can't turn this off. If you want this software, don't uninstall it. If you don't want this software, you can uninstall it, or leave it alone, it's up to you.