An environment is one or a group of gateways of any given platform. You might have a set of synchronized gateways in your on-prem data centers and another set of synchronized gateways in your private cloud. In this case you would create two environments within the API Control Plane.
Stages are an element of an API’s lifecycle. During development you might run the same API in different versions in different stages. So, you might run version 1.0 in production and 1.1 in development. The API Control Plane at this time has built in support for production and non-production (aka development) stages. Every environment is assigned to a life-cycle stage. This means it is not possible to create an environment that spans two stages.