I wouldn't call pre-WWI and post-WWI "roughly the same time period". Not by a long stretch.
The length of time between them is not relevant in this case. What is relevant is the events that occurred between them.
Like the pre-atomic age and the post-atomic age. The events themselves in Hiroshima and Nagasaki were relatively short-lived. But their impact on this world greatly exceeded the time immediately before those two events and the time immediately after those events.
This is all pretty clearly laid out in the historical literature that you yourself linked to. You don't seem to understand how art movements work; there is not a firm dividing line when one ends and the next begins.
Beyond that, the question was about why people mix the two. Your nit-picking about how we should divide history is irrelevant to the discussion.
And I lived in Brussels, Belgium for almost eight years, in a house that was built in 1910 (according to the numbers formed into the bricks), and I lived about two blocks away from Hotel Horta. We have several coffee table books on Art Nouveau and Art Deco, some of which you can no longer find.
So, I am very well acquainted with both styles and when they were common. I also make a point of reading articles at any links that I include for reference.
This is the subject of the grandparent post that I was replying to. Yes, in actuality, they overlapped a bit, and Art Nouveau waned as Art Deco rose – although again, this is not so clear cut in other art fields as it is in architecture; e.g., jewelry or furniture.
And while Art Deco got started before WWI, it didn't really take off until after WWI.
Just like Art Nouveau that got started in the 1890s, but didn't really take off until after the International Paris Exhibition in 1900.
Both styles took several years to get started and really take off. And Art Deco didn't really take off until after WWI.
Art Déco first appeared in 1910, and became much more popular in the 1920s, after the end of WWI. See https://en.wikipedia.org/wiki/Art_Deco