Ok y'all, I have questions. It appears to me that the ads for these 2 watches are really similar. To quote Mugatu: "I feel like I'm taking crazy pills!!". None of the ads mentioned (there are a couple more Trained Nurse ones in the DB) list what color the sweep second hand was.
Miss Air Warden:
Trained Nurse: 
Both have sweep hands that are dark, there was a later version of the Nurse that added a red sweep:
Is it just me??
No, it would seem there was a change in the name during the war years?
One can assume the name switched back post war, date of manufacture would determine the model name.
In reply to No, it would seem there was… by FifthAvenueRes…
Potentially---the database only has 1941 ads for the Trained Nurse and 1943 ads for the Miss Air Warden. I'm going to do a ridiculously deep dive into newspaper archives I have access to for my real day job (lol) and see what I can come up with.
Yes I agree probably a name change for the wartime, there were a few of those. Also sometimes Canada had a different name to America.