Also, this is completely missing the point here:
> Don't want your name tarnished? Don't park illegally.
It's not about reputation, it's about privacy -- and safety.
"Criminal" means in the criminal code, but both are illegal. I think that you don't have a right to privacy for either because it obfuscates the application of the law. Indeed, the Japanese government can query the Ontario government to get a list of transgressions that you had while driving a car in Ontario (I know this because they did so when I converted my driver's license to a Japanese one -- and they didn't need my consent).
I think OP's use of the term "criminal" is a bit loose, but I would be surprised if you have any right to privacy for a a fine levied due to a legal infraction. Whether or not you should have a right to privacy is a completely different conversation...
Aside: It was important to me because many years ago I inadvertently drove while suspended. I had an unpaid ticket that I had forgotten about and my license was suspended. The suspension got lost in the mail (first a postal strike and then the delivery person put my mail in the wrong "super box" -- I eventually got it months later). When I was first getting my visa for Japan, I needed to find out if this was a criminal offence or a highway traffic act offence.