In relation to those vessel tracker and marine traffic websites they work by volunteers feeding in the VHF AIS data frequency exactly like flight radar 24 so if there out of coverage of the nearest feeder it will only show the last position of the vessel when it had coverage.
I believe you can pay $300 a month to marine traffic and get the vessels position by satcom.
The ship tracking websites work in the same way as the aircraft tracking ones, i.e. using volunteers. But it seems unlikely that there are any volunteers in the middle of the Indian Ocean so those tracks must have been uploaded by a ship via satellite.
There are sometimes errors in the AIS data and some aircraft and helicopters, particularly SAR ones, transmit AIS. These tend to only have a MMSI, i.e. no IMO.