@Gregor *********
I think they are actually trying to reduce the complication. Yes OK sometimes the terms are wrong (visa vs extension of stay, admitted till date, etc), but if they told people to follow the validity of their original visa, people would think they can stay longer than they can. They would get confused and NOT check the stamp. This happens all the time. So focussing on the stamp (as they mention and call it a visa) is a good strategy. Sometimes the perfectly correct terms don't really matter, as it is as clear as day on the stamp when you have to leave. If I am on an extension of a visa, I still say I have a visa, and so does everyone else.