I would argue that referring to these milestones as "phases" would be preferable to "stages." This is because "staging" is already a more prevalent term in use in the industry.
Staging refers to a specific environment used for walking through testing the deployment process. It is distinct from the QA environment used for bug testing and sanity checking and testing environments used for User Acceptance & integration Testing (UAT). All of these could be considered types of test environments.
The origin of this term comes from theater in which actors will walk through a scene - often stopping to adjust, clarify, and note physical positions on stage. This is often also referred to as "blocking" in theater.
Thus, if you call these milestones "stages" you could end up having a "staging stage" and for the sake of clarity, "staging phase" or "staging milestone" would be preferable and more prevalent. These are the more common and customary terms, driven by the terminology of project management.
I would typically dis-recommend using the term "testing" to refer to an environment, because it can be confusing as to which testing environment you are referring.