Category: Heathrow Connect
Introduced in 2006 as an alternative to the Heathrow Express, Heathrow Connect is a stopping rail service calling at a number of stations between Paddington Station and Heathrow Airport. Travelcards are valid between Paddington and Hayes and Harlington, but not between Hayes and Harlington and the airport.
According to Wikipedia, passengers transferring between Terminals 1/2/3 and Terminal 4 can use the Heathrow Connect service free of charge.
Stops (in order) that the service makes (view them on a map):