Application = ordinary subnet.
System subnet = no cycles need to be paid for running canisters, some more generous execution limits. Used for NNS and II subnet
Verified application = leftover idea from ~launch time. Conceptually it would have been similar to subnet rental. Today it is the same as an application subnet
I have not heard anyone talk about concrete plans about other subnet types. The future could hold e.g. storage subnets or GPU subnets as new types.
I haven’t heard of any specific plans. If you have a good reason to make a subnet of a new specialization feel free to start a discussion. I suppose the swiss subnet is similar, but since that one will go through the subnet rental canister (at least according to this post, not sure if that’s still the plan) I’m not sure access to it will go the usual CMC-managed access control route.
This post explains how authorization works at the moment. There is no other access control/authorization mechanism in place.