Ok, that definitely works, assuming you set your process up that way. In my mind, "deploy" starts with build and targets a single environment. Eg: deploy to staging, deploy to production. I've been working with too many clients these past few years who do it that way. One has a real TeamCity CI setup, but they rebuild for production too.

Way back in the day, I helped push my company towards a process where build artifacts were tied to specific commit ids (SVN, back then) so that everything that reached production could be traced back through QA and Development. So, basically the process you described. No containers back then, of course, and no VMs either. We had real servers in our server farm.