Don't know about where you are, but in Ontario Canada (the only place I've gotten in enough trouble to care about the difference ;-) ), there is a criminal code and the highway traffic act. There are illegal things that you can do in your car that may be in either or both areas.

"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.

In WA at least all traffic offenses are public record. You can go search court databases by either name or license plate to get the full details of any tickets and charges in that system.