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Yes this is definitely foggy when you just start exploring / thinking about this.
I think of a multiplicative comparison as scenarios where finding a scale factor makes senseâ€¦ for example, two different length pieces of wood. I can find a multiplicative comparison between them, however scaling them doesnâ€™t seem as natural / necessary.
A composed unit, on the other hand, has two or more quantities that feel natural to scale in tandem. For example, scoops of hot chocolate mix and glasses of milk. You could find a multiplicative comparison, however it wouldnâ€™t be a scale factor, that would actually be a rate!
Whew! Crazy stuff, right?