If you and I are both running "Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.8) Gecko/20051111 Firefox/1.5" we are both running the "same application". But we are running two different instances of two different installations on two different systems. If I were logged in twice to the same machine in different X sessions, I would be running two different instances if the same installation of the "same application".

So unfortunately, saying that you're viewing "the same applications on two screens" isn't unambiguous. And no, I can't tell you how to say it unambiguously and concisely.