In terms of definitions, generally cosmos contains everything.
Universe is our local observable space-time with the earliest event we can detect being the big bang.
Universe is our local observable space-time with the earliest event we can detect being the big bang.
So if we observe something beyond what is currently observable, would that not become observable and thus part of the universe?
Transitivit would say yes. If A implies B and B implies C then A implies C. That is, if you can observe A and that implies B, then you can observe B. Which makes it observable, no?
For now we're stuck in our universe, we know it's expanding (in something, potentially). So we preemptively give the name "cosmos" to EVERYTHING. It's entirely possible that cosmos is equal to universe. But it's also possible there are other universes out there, or something entirely different.