Flight radar is a combination of FAA data and civilian receivers. The FAA data is a world wide compilation consisting of commercial and most corporate aircraft. Civil aircraft are generally phasing into this database by requirements to upgrade or install for the first time more sophisticated transponders. The FAA data is updated about every 3 minutes as I recall.
Where the civilian transponder receivers fit in is primarily with civil aviation as these aircraft are not likely to have satellite communications. These receivers can fill the gaps so to speak for civil aircraft generally and to give more rapid updates in high traffic areas such as airport approaches. The receiver range can be 50 miles or so as I recall but varies quit a bit depending on hardware, antenna and geography.
In between receiving data updates, flight radar displays an estimated position based on speed and heading from the most recent data update. The data box in the sidebar off the map has the speed, heading, altitude, etc. if the most recent hard fix. You can see it change every few minutes.
That youtube video was intriguing. It showed the positional and flight deviations were radically different between the “live “ data and the archived data that I think he said was about 24 hours later. Why the changes?
FAA radar data is only supplied for aircraft in US airspace. Everywhere else in the world, the data comes from aircraft ADS-B transponder data, which is picked up by internet-enabled receivers. These are often peripherals attached to privately-owned PCs used by civilian Ham or radio enthusiasts. ADS-B is present on a limited number of airliners (about 70% of European/Asian, and 30% US; largely Airbus, some of the Boeings). The majority of civil aviation actually is not covered by this, nor are most smaller business jets, so all that you see are the big airliners.
I suspect the confusion over the term “flight radar” is coming from my example of the website by the name “flightradar24”. It and several other flight tracking websites use similar terminology, though their graphic displays do not get any direct input from any ATC system.