An FPN (Fixed Penalty Notice) allows the police to dispose of a criminal matter without the bother of cautions, charges, all that guff. You get your penalty notice, pay it, and you should hear no more - meaning you don't get a criminal record. You have the right to have your case heard at the Magistrates Court if you really want and the Magna Carter NuttersTM generally do.
A PCN (Penalty Charge Notice) allows the local authority to dispose of a civil matter in a similar manner.
If you are being given an FPN by the police, failure to pay it will see you hauled up in front of the magistrates court, fined, and landed with a disclosable criminal record. Failure to give correct details may be a separate offence. They may ask for your details if they suspect a crime has been committed. Declaring yourself to be Mickey Mouse resident at Buckingham Palace is not likely to end well. Be co-operative and pay up.
If you are being given a PCN by a random civil officer, failure to pay it will see you going through a torturously long procedure involving appeals to an Independent* Adjudicator, who will usually uphold the penalty, and after that you can be taken to the County Court where eventually you may face a CCJ, which will affect your credit rating. However, random civil officers have no power to detain and no power to demand to see ID. Riding away from them is an appropriate course of action although it will piss them off enormously. If they try to detain you physically you can sue them. But it's easier to ride away if you can.
*ish