External Logitech keyboard recognized as Apple keyboard

I have a Targus docking station connected to my MacBook pro. The external keyboard is from Logitech.

The computer does acknowledge the existence of an external keyboard, but some keys are wrong. When I try to change the keyboard type, and am asked to press the button directly to the right of the left shift key (which is <>) there is a message saying that I have pressed a key on my Apple keyboard, and please use the keyboard that is not recognized. If I skip it just skips and I'm back to default. If I press OK the settings app hangs. It's like the computer understands that there is an additional keyboard, but thinks it's an Apple keyboard.

The result of this incorrect recognition of my keyboard is that some special characters that I use often are not in the right place and I sometimes have to try several out before finding it, as it's hard to remember.

When I connect my Mac Mini to the same docking station, MacOS recognizes the keyboard correctly and sets the keys right. Having different keysets with the same keyboard for two Mac computers is not optimal.

This is driving me mad! Please help!