No, the first mailed fine would be the payment reminder from the collection agency with some additional fees attached, after which it will move to proper collection. This applies only to parking fines issues by the city/municipality. Private parking spots have a different system, but they usually also rely on just a note on the windscreen.

I think it's part of the Finnish society often resorting to an honor system in these kinds of things. For private operators also due to the fact that previously the fine couldn't be assigned to the car owner, and had to be assigned to the driver personally. Nowadays a lot of places just automatically scan the plates and you pay either via app or a website.

Infuriatingly getting cars towed is also very difficult in finland, and I mean multiple layers of red tape and a few weeks of time spent difficult. Due to the fact that the tower is responsible for any sustained damage, that can be as little as a scratch in wheels or similar, and can't bill the car's owner unless they've been duly notified, it's practically an impossibility for anything other than abandoned vehicles. If somebody else is in your spot you just have to find another one, even if you're paying good money for it.

The ticket stealing thing no longer happens AFAIK, since the PEO just scans the plates to see if you've paid for parking nowadays.