In principle, the router can technically replace your Internet box (except for the Wifi), BUT this is only possible if your Internet provider allows it. Specifically with Swisscom it is difficult with fibre, but you may have to buy your own SFP+ module and correct configurations without official support from Swisscom - with suppliers such as Init7 you would have a free choice of router, there it would not be a problem.

Behind your Swisscom router always works, but then you have double NAT, theoretically not full throughput and minimally more latent.

The different gateways can be compared online: https://ui.com/cloud-gate...

So, the difference between the Cloud Gateway and Gateway is that it is not a Unify server. You need something that manages your Unify devices. I don't know how it is with Swisscom. Normally you have to put the router in bridge mode so you can use your own router.