finder on iMac won't recognize iPad but will charge it

Which macOS version is the iMac on?

What iOS versions are the iPad and iPhone on?

I can't put my finger on the issue without more details, but it sounds like maybe the iPhone is being sync'ed with Finder in some other way (wi-fi, bluetooth, iCloud) besides the cable connection and the iPad is not.

Have a look at > Sync your iPhone, iPad, or iPod using your computer - Apple Support to see if that helps you get the iPad sync'ed with your iMac via the cable or other method.

dirt or lint in the connector can cause the connector not to have a full connection to all the pins, cleaning it out with a match or toochpick would usually resolve it, but of cause it could also be a damaged connector in the ipad