Departure Frequency coverage area

When selecting to be an ATC Dperture controller on the playground server, take “SoCal departure” for example, I was shown a starting screen around San Diego airspace and the surrounding 3/4 airports and the airports names are green and show (App) which in guessing is for approach.

But around the LAX area and the surrounding airport the names were also green and showed (App), and I had several aircraft contact me for departures around that area but I didn’t know if they had contacted the wrong frequency.

Is there separate areas within regions for departure controllers or are they meant to deal with departures from every major airport?