So based on what I've read here alongside some perusing the internet and Wikipedia, the general focuses of various movements can be summarized as:
Modernism - austere, clean, lack of gratuitous adornment, using material to provide texture as opposed to form. Essentially a backlash against Deco/Nouveau's opulence. Started early 20th century-ish, gained real traction post WWII, continues at various levels in contemporary design depending on designer and application. MCM is a subset thereof.
Post-Modern - backlash against Modernism, bring back the details! Revival of some (not all) classical design concepts, as well as introducing asymmetry, organic shapes, brutalism, etc. as a way to add depth and interest to contrast modernism's lack thereof. Gained traction in the 80's (?), and also continues today depending on designer and application.
Seem about right?
What I struggle with is when I'm browsing a store or looking at pictures online (this thread for example), how can I distinguish between various subsets of Post/Modernism? Are there defining visual characteristics that can reliably distinguish Danish from American from Bauhaus? Or is that an issue of doing my homework and learning individual designers' styles and history?