Yes, my understanding is that the salient characteristic of a sushi knife is being made of carbon steel and having a single beveled edge. The best ones can be really expensive and they rust very easily so caring for your knives is an essential part of the sushi chef tradition.
downside of the carbon-steel knives: as you mention rust and tarnish … and more importantly - a nasty kind of metallic taste/smell to it … that imprinted itself on some acid food like fruit like crazy.
my wife was always fast (and right!) to ask me if I cut XY and Z with that knife - and I agree you could taste it.
so, in short, I had to retire the Opinel No 10 from kitchen duty
… no-more-knife - happy wife!!!
one of the big pluses of carb-steel is - you can very easily sharpen it … Just by stropping 1000grain sandpaper twice or 3 times and you were off to the races …
Mostly that isn’t an issue for me, but the exception is citrus fruit. I cut those with other knives.