IMHO the most discernible difference between beer and wine is the use of grain and grapes/fruit. Beer tends to be grain based - think Reinheitsgebot. However it can be difficult to decide if cider is a beer or a wine - maybe a fruit beer? Carbonation per se seems to be no guide, as champagne is fizzy - more so than most beers. Use of hops seems to be peculiar to beer - but there are reports of one or two wines made with hops. So that may be a good indication but is not a defining factor. Most beers have added yeast and most natural wines are fermented with the yeast naturally on the grapes. But with modern industrial processes that tends to be lost in mass production methods that add yeast to both brews.
I suppose the obvious defining factor of "beer" is that it is made from malted and mashed grain. The sugars need to be converted from the starch stored in the grain to be able to ferment. That conversion might define the brew as beer. Wines are made from things that already have fermentable sugar and so no conversion is needed. That definition would make cider an "apple wine" and sake a "rice beer".
Barley in its dry stored state has little if any natural sugar that can be fermented by yeast to produce alcohol. It has to be malted and mashed for the sugars to be converted ready for fermentation. Could one polish barley grains and then treat them with Aspergillius mold like rice? Err, possibly but why?
Sake is made from unmalted rice grain. The startch in the polished rice grain is converted to fermentable sugars with the help of Aspergillus mold. Then the fermentation to produce alcohol is done with Saccharomyces. So one might say sake is like beer as the rice must be "prepared" to ferment.