The 3nm quoted in the ANO and LASORS is for the purpose of defining the privileges of a FI(Restricted) who may not send a student on their first solo cross country i.e. more than 3nm from the airfield.
For the purposes of gaining a licence, cross country flight is regarded as a flight from A to B or a flight from A to A involving one or more preplanned turning points. Thats why it is recommended you list turning points in the log for flights claimed for this purpose. Once you have a licence, there really is no formal definition of a cross country flight.