Why join together two decades into one category? I call that whole era the "war years": pre, during and post. The mainstream popular music was swing jazz, spanning both decades, and the mainly relevant mark is to realize weather a tune was playing before, during or after the war.
In the early 30's the "silver screen" tried to help folks ellude the depression, with lavish musical productions, then the screen turned black, forewarning the war; during the war it portrayed mostly the heroes and the fronts, and after 45, the party began - or restarted.
Some people do not appreciate the "musical" film genre, because musicals do not portray reality. For the "war years", I would like to point out the music of a non-musical film, portraying hard reality: Casablanca. In response to german soldiers singing their hymn in Rick's Café, the french patriots wring out "Allons, enfants de la Patrie...", shutting out and up the germans. As for those to whom the war had just meant frustrated love affairs..."You must remember this, a kiss is still a kiss"..."it's still the same old story, a fight for love and glory"..."no matter what the future brings...as time goes by!"
In terms of "evolution" the fact I believe stands out in the 40's, is the definite widespread acceptance that in music, rythm - tempo or "beat" - was at least as important as melody. It had been before, although not as widespread, with jazz (and before that, with spirituals and blues, which had been around since slavery). We owe it all to the intermingling of african and european cultures, that went on in the american melting pot, for about 300 years. Swing Jazz and the "Big Bands" (Glenn Miller, Tommy Dorsey, et al) stepped it up and refined it, exploring many tempo variations and allowing entertainment of the notion that syncopated rythm music could ever become known as classical. Both popular and erudite music evolved. If only folks then had any idea of what was to come next, even if only in musical terms!
Betty Grable - There's Danger In A Dance
Fred Astaire - Cheek To Cheek (Top Hat-1935)
Fred Astaire - Let's Call The Whole Thing Off
(Shall We Dance-1937)
Glenn Miller - Pennsylvania 6-5000
Fred Astaire & Eleanor Powell - Broadway Melody (1940)
Humphrey Bogart & Ingmar Bergman - Casablanca (1942)