vague is to do with how you express yourself - his account of what he did that day was rather vague fuzzy comes from material which is not smooth, like felt and is used to mean 'vague in outline' or without clear boundaries you can also say that someone's thinking is fuzzy,but it would sound odd to say someone's story or account of a situation was fuzzy. actually quite hard to differentiate when I think about it.

Have a look at each word's etymology to see the history of each word. That will tell you a lot about the nuances between each word. You'l also see that one of the words refers to something physical and tactile. We can take physical properties to describe abstract ideas, or to draw analogies. I'll let you do the research yourself. Tell us how you go.

The easiest way to think about it: 1) Fuzzy is more informal (but it's not rude) and 2) Fuzzy means "very vague". "I have only a vague understading of the problem" means I know something about the project, but not very much. "I have only a fuzzy understanding of the problem" means "I hardly no anything about the problem"

The two words can often be interchangeable. Perhaps the best explanation I give is that you would be better suited using "fuzzy" when talking with friends or family, rather than in a professional setting. Although both words could be used in the work environment, "vague" sounds more professional. Hope this helps!