Even though sites such as RTT pulls from systems that show where the train is?
The level of reporting varies massively around the network. In track circuit areas with berths for each station the signalling system will describe where trains are relative to stations and the arrival/departure times won't be significantly out. The trains won't be removed as an actual report is expected so if a train stops unexpectedly it will be marked as delayed. For short branch lines like St Albans Abbey the whole branch might be a single track circuit or other form of block so the signalling itself doesn't know where the train is precisely. If the train is reporting its position via GPS that will be used for actual times, however the equipment might not work or may drop out so estimates are sometimes all that's available. Other locations the time may be reported by the signaller or another member of rail staff often with a delay between event and report.
My rough understanding is there are central railway operational systems like TRUST which are from the days of mainframes, intended to be accurate historical record with no predictions. There's then the central information system that collate from sources like TRUST, other automated systems, manual input from staff which is used for passenger information and provides predictions. Websites will use the central information system (Darwin) for departure boards, cancellations and delays. At stations, the information system will be from one of the suppliers who won't override the Darwin predictions but might add additional details like brand of train/platform zones or reword things like cancellation/delay reasons. Platform numbers are a bit more complex so ignoring these.
RTT doesn't use Darwin, the license for the open data version of the information system is pretty restrictive including being forced to use its predictions. It will rely on the same sorts of sources as the central one for actual times and can provide a more complex picture than would be acceptable on a platform information screen. Some operators provide information to RTT most notably formation/unit information. Similarly operations have decided to report some information onto Darwin where others haven't. Similarly some operators have put different levels of effort into configuration of central systems to improve train time reporting, predictions and warning of platform changes.
To give an idea of the level of variation: SWR reports formations to RTT, doesn't include train length on Darwin does on CIS. Southeastern include train lengths, toilet locations (and reported status) & expected train busyness on Darwin and CIS, doesn't report formations to RTT. Avanti reports formations to RTT and coaches/toilet locations to Darwin. Thameslink doesn't report formations to RTT and only train length on Darwin.
