South Yorkshire PTE pass holders may travel for free on rail services within South Yorkshire (and to Denby Dale, Darton, Moorthorpe or South Elmsall in West Yorkshire). Trains must call twice in SY, which means Northern, TPE, plus XC (and the odd EMT) services between Sheffield and Doncaster. No East Coast train calls twice in SY so their trains are outside the scheme. Additionally on Northern's services (ONLY) Pass holders can travel to/from Leeds or Huddersfield and to intermediate stations on THROUGH trains. Change of train to further WY destinations isn't allowed. Passes are valid from 09.00 (M-F).
WY PTE Pass holders have to buy individual journey rail tickets (after 09.30) at a reduced fare, but only to the WY boundary. They cannot travel onwards to SY without buying a full price ticket.
ALL of the above only refers to RESIDENTS of those areas and not elsewhere.
However, in order to show how generous the Council Tax Payers of South Yorkshire are, our PTE does allow any English Pass holder to sample the excellent Sheffield Tram network for free (after 0900), as well as the buses.
PS - None of the PTE schemes is listed on National Rail's web page