why does airport utility show 7 wireless clients when we have 1 iPhone, 1 iPad, 2 MacBooks, 1 printer?

You may have an Apple Watch, security system or doorbell, a lighting system, television, refrigerator, oven, garage door, or any number of other devices that connect to the WiFi system, but you have forgotten about.

It is possible, but unlikely, that you have an uninvited guest or two on your network.

AirPort Utility displays the number of devices connected to your network along with a clue about the name of the device. If the name of the device is not displayed, the IP Address or WiFi ID is displayed.

Other stand alone applications like iNet Network Scanner.........https://apps.apple.com/us/app/inet-network-scanner/id403304796?mt=12........are available for a fee that will probably tell you a lot more than you want to know about your network.

If you are convinced that you have uninvited guests on your network, change the WiFi password on your main router. You will then have to reconnect all of your WiFi devices again using the new password. Only give the new password to those people who you trust to not give it to someone else.