TN-S is the system which was installed as standard in urban areas years ago. It has a completely separate earth path back to the sub-station, generally via the armor of the underground supply cables (although TN-S was also run overhead on occasions). The main earthing lead from your consumer unit will be connected directly to the earth terminal provided by the power company.
TN-S diagram
TN-C-S is the newer designation for
PME (Protective Multiple Earthing). In this system, your main earthing lead is connected directly to the incoming neutral of the supply at the service block. There are different physical arrangements of connection due to the age/style of service. To the untrained eye, it may be difficult to differentiate between TN-S and TN-C-S with some types of service equipment, but there
should be a sticker on PME systems telling you that PME is in use. (Note that PME systems have strciter requirements for bonding than TN-S.)
TN-C-S diagram
TT systems, as you say, have the house earthed only locally, and are easily identified by the fact that there will be no separate earth lead running anywhere to the service on the supply side of the meter.
TT diagram
Combinations of systems can be found within an installation. For example, a house could be on a TN-S supply but have a garage or outbuilding which has been wired as TT with its own independent earth.
Houses can also use a mixture of systems from a common distribution system. For example, PME was originally installed only in rural areas where other earthing methods were deemed impractical, but in recent years its use has become much more widespread. In my local, rural area, the PoCo has installed the extras earthing required along all routes and will provide a PME/TN-C-S connection to any house upon request. The majority of homes, however, are still operating under their original TT systems.