Typical homeowner has curbside landfill trash, co mingled recycling certain plastic/metal containers, green yard waste, battery waste, oil and oil filter waste.
Same system here, most haulers provide two large (96 gallon wheelie) bins, one for trash, one for mixed recyclables. But our recycling will ONLY take corrugated cardboard, news print, aluminum cans, glass bottles (but not other forms of glass), and type 1 plastics. They will not take the roughly 400 plastic bags we drag home from the grocery store, the miles of bubble wrap we receive from Amazon every week, or really almost anything else marked as "recyclable".
Yard waste here is kept on your own property, or you can haul it to a mulching facility yourself, at least out in the townships where we live. Most boroughs would have a program for picking up or receiving yard waste separately.
We're left on our own to deal with batteries and oil, which means 99% of people probably just find ways to sneak the stuff into their regular trash. I usually stay friendly with someone who has a waste oil burner, that's how I get rid of all my used oil.
Not curbside is e-recycling, hazardous disposal including paint, pesticide, lawn and garden chemicals, medical sharps, pharmaceuticals and firework/explosive disposal including bullets, special transfer station for things like asbestos siding and pressure treated wood.
Our township has a hazardous waste drop-off day once or twice per year, but it seems I'm almost always away on travel or unavailable on that one day. I usually pour any paint or similar chemical into a hay bale and leave it out to dry, then burn or put the hay bale out at the curb, as it's leagal to dispose of cured paint... just not liquid paint.
Never had any medical sharps, so I don't know how we deal with them in residential waste. The few times I've received medication in a syringe, they were of the spring-loaded type that retract and cover the needle automatically, so that they can be tossed into regular trash (residential only).
Pressure treated wood gets burned in the back yard.
Guess we lucky we don't have trash pickup we are on our own. No transfer stations either and the landfill is an hour. Good small business for trash haulers or folk that like to dump on the logging cuts.... (wish is was legal to shoot them)
We have organized hauling in just a few local towns, but most just contract directly with an independent hauler. Usually, one takes note of which hauler their neighbors are using, and then sign up with the same, as you tend to get the best rates when everyone on a street uses the same hauler.