TfL's records, which are reflected in its single fare finder and the Oyster Fares and LT Fares websites, are definitive when it comes to determining what you will be charged for PAYG journeys. That's because the charging is done based off their fare records.
The National Rail operators keep their own copy of these fares, under the 'fake' ticket type codes PAP, PAC, POP and POC for peak and off-peak fares, respectively for journeys where PAYG Oyster as well as contactless are accepted (PAP/POP), and ones where only contactless are accepted (PAC/POC).
These fares are reflected in the fares data disseminated by BR Fares, and are used by National Rail journey planners to give an indication of what you will be charged if you use PAYG instead of buying a conventional ticket.
However the National Rail copies are often not kept up to date - as in this case, where TfL increased their fares in March, but most non-TfL operators didn't. So presumably someone forgot that they needed to increase the PAP/POP/PAC/POC fares to match what TfL are now charging.
It's quite an unsatisfactory situation to be honest, because you can't get an accurate comparison of the cost without checking both a National Rail journey planner and a TfL fare finder.