大概三个礼拜之前被警察拦下开了罚单，昨天在check if you have a fine上查了，今天收到回复说 You have no fines in the Ministry of Justice Collections database for the identity details you have provided.
A fine is imposed by the Court whereas an infringement fee is imposed directly by a prosecuting authority (eg, the Police or a local body).
You can be fined by the Court as a penalty for a criminal offence (e.g. for drink-driving, theft, or vandalism).
An infringement is money you have to pay for breaking the rules e.g. the Police can give you an infringement notice (a ticket) for speeding, and the city council can give you an infringement notice (a ticket) for parking in the wrong place or for too long.
If you don't pay an infringement fee in time, it gets sent to the Court for collection and becomes a fine.