Got it. The ringer volume is on Settings > Sounds & Haptics> Ringer and Alerts
The volume control on the home screen and on the Control Center are the same control and it affects only music and perhaps a few other things like Siri (haven't been able to investigate yet).
You can change this to make it work like deggie's phone by turning ON the "Change with Buttons" option. Then, the two controls will be different - the control on the home screen will affect the ringer and the control on the Control Center will affect music. If you operate the side buttons while the phone is ringing, it will correctly turn the ringer off without regard to the haptics setting.