Azuki was a brand of bikes imported and distributed by a Louisville, KY bike shop. Or so it says, somewhere on the internets. Don't know about a connection to Nishiki, but possibly Azuki was simply a rebranding of Nishiki models. Bikes look similar and assuming similar condition obviously $80 is a better price. Careful looking and patience will certainly bring you a better bike though: chrom-moly frame, downtube shifters, better components. Should be able to find that for under $100 and in good condition too, if you can wait. Good Japanese brands to look for: Miyata, Nishiki, Shogun, Lotus, Centurion. All had a full line of bikes up from entry level up to very high end, and there are a lot of these bikes out there.
I bought a bike in '76 new just like it, a different brand, same bike for seventy five dollars. It was an inside deal. For eighty it's ok but at any price it's not a rewarding ride. Hi-Tens. steel frame, cheap drive train , steel wheels etc. all work in concert rendering performance noticebly infererior. Not being a snob here, it just that a few bucks more (or less), one can find a better bike that'll ride and shift much better. You really WILL notice the difference.