The 501 Queen runs throughout the day in both directions. Some cars short-turn at Humber Loop, while the others go through to Long Branch. Service is on 5 to 10 minute headways from about 6 AM through 1 AM. There is also a blue night line service in the wee hours.
The 508 is a “tripper”, which supplements the 501 from the west end of the route to downtown in the rush hours, i.e. eastbound in the morning and westbound in the late afternoon. The AM and PM routing are slightly different only because of how the cars turn in the downtown core at the end (AM) or beginning (PM) of the runs.
(To expand on my previous post, the term “tripper” goes back to the earliest days of the TTC, if not to its pre- 1921 antecedents, though it is rarely used today. The term refers to a single trip extra run during the rush hours.) Until about 25 years ago car lines were known by their route name and destination, not by a route number, e.g. “Neville Queen” or “Kingston Road Tripper”
To understand the full range of service look at the Route Description tab for each route in conjunction with the Map tab.