In addition to paying the fixed penalty, [unless the fixed penalty clerk is satisfied as to your identity] you must provide the required identification details to the fixed penalty clerk - this is generally referred to by the polis as your "licence details" - name, date of birth and driving licence number.
In England and Wales at least, seemingly the most common reason for an attempt to accept a COFP to fail is the failure to read and comply with this separate 'requirement', although personally, I am of the opinion that when paying the fixed penalty online, the information you provide satifies these requirements as your date of birth is part of your licence number.
Logically, either you haven't read the fixed penalty offer properly and missed that part, or it is technically possible that polis scotland pooled their brain cells and issued both to the same person, who decided that providing you identification details to the fixed penalty clerk is not a separate requirement to providing those same details to the fixed penalty clerk when paying the fixed penalty.
For the sake of completeness, the points are applied to your licence record by the DVLA when the fixed penalty has been paid and the identification details (so they know whose licence to endorse) are received.
