Just a quick note about the four stations at Heathrow - 
*Heathrow Terminals 1, 2 & 3 railway station - served by mainline Heathrow Express (Class 332) and Heathrow Connect (Class 360)trains
*Heathrow Terminals 1,2,3 tube station - served by London Underground Piccadilly Line
*Heathrow Terminal 4 railway station - served by mainline Heathrow Express (Class 332) only.
*Heathrow Terminal 4 tube station - served by London Underground Piccadilly Line.

All four are separate stations, although both pairs share the same names!