Is silent mode truly a silent mode ?

Most likely you have a phone that was intended for sale in Japan or South Korea, countries that require that cameras make a sound when taking a photo.

Not on the device. You can sell it and purchase one that does not have that restriction if you like. However, that restriction is hard coded into the device and cannot be disabled.

One thing you can do is hold your finger over the speaker on the bottom of the phone. It’s to the right of the Lightning port

You're welcome.