I've recently had some very intense discussions with what are mainly people too young to have any first-hand knowledge of this.
To my recollection having both used and sold machines during this timeframe; the first Mac was the "Apple Macintosh M0001" and shipped with 128k of RAM. The next was the M0001W, what we in the day called the "Fat Mac" and it shipped with 512k of RAM but was the same machine but with the memory Apple wanted but was not ready to ship with. Both of which had a rear case badge with "Macintosh" These machines are what I've always known as "First Generation" compact Macs. The machines with an actual rear case badge of: Macintosh 128K and Macintosh 512k are ones that I've always called "Second Generation" machines and came out later.
I don't own any 128k or 512k badged machines so can anyone verify if they are identical or not to the Macintosh and "Fat" Macintosh? I recall the logic boards not being the same.