'Pitru' sabda means protector or ancestor in general. Pitrus belong to different classes. Pitrus of brahmins are called Somapas, those of kshatriyas are called Havirbhuks, those of vaisyas are called Aajyapas and those of sudras, Sukaalis. Their status also depends on how they have lived their life on earth. Those who have performed yajna become Somapas, those who have performed only haviryaga ( rituals where only rice is offered to Devas) become Barhishidas and those who have not performed any yajna become Agnishwathas.
The immediate three generations of pitrus - father,grandfather and great grandfather are called asrumukha pitrus and the three generations above them are called naandimukha piturs. The yearly sraadhham, amavasya tarpanam etc. are meant for the immediate three generations above called asrumukhas. "Naandi" performed as part of upanayana etc. are meant for the naandimukha pitrus. There is yet another group called kaarunika pitrus which includes friends and relatives.
The lord of pitrus is Yama. However the group of father exists in the from of Vasus, that of grandfather exists in the form of Rudras and that of great grandfather exists in the form of Adityas( sun). The Vasus are eight in number, Rudras eleven and Adityas twelve. The brahmin fed in pitrusthana during sraadha is nominated as vasu-rudra-aditya swaroopee meaning of the form of vasu-rudra-aditya. The second brahmin is of the form of viswedevah who is the protector and escort to the pitrus during their journey to earth to take part in the sraadham.
There are 96 sraadhas to be performed every year in addition to the tithi sraadham which is in fact the only one being observed these days. There are still people who perform all the 96 sraadhas at least in the form of tarpanam as in amavasya. These sraadhas are amavasya(12),Samkramana or the first day of the solar month(12), Manvanthara (14), Yugadi(4), Mahalaya(16), Vyathipatha(13), Vaidhruthi(13), Ashtakanvashtaka(12). The details of these are available in standard panchangam. See the huge gap between what is ordained in the sastras and what is practised in reality.
The above concepts and practices are from the smrithis and are different from what used to be followed during Vedic times. A yajna called pindapitruyajna is what is ordained in the srouta or Vedic text intended for the pitrus