What is the difference of a British Citizen and a British born person?

For purposes of education in this case, the children will be treated as like any other student with a British pport, or Indefinite Leave and have lived in UK for at least 3 years, or EU citizen. There should be no worry, and the government's new policies do not apply in this case. I have held a British pport for 1 year, my wife has ILR, my 19yr old son has ILR and has lived in UK for 3 years and he is going to Oxford this September.