NYC has the FDNY, voluntary agencies, and private companies.
The "voluntaries" are called such because they voluntarily participate in the FDNY 911 system. These are primarily the hospital based services. I used to work for one of them in queens.
They follow all the FDNY rules/regs. Most if not all also follow their scheduling to a degree. 8 hour shifts. Tour 1, first tour of the day, begins the night before. Start time varies among units. can be 2200-0600, 2300-0700, etc. Tour 2 is day shift, tour 3 is evenings. FDNY sets the times for the units. Doubles are allowed. They all have designations, based on batallion. 51C, 47X, etc. Each unit is assigned a specific radius, and you get dispatched to any 911 calls in that area, or whatever you're close to. Units can manage to wind up far away from their area. For the most part you'll stay in your borough.... mostly. Pay varies, as it's set by the hospital. You will make more per hour than FDNY/ As an EMT, with only transport and volunteer experience, my starting salary was around $22/hr. Medics started about $26/27 i think. However it's much harder to get full time at these places. They tend to have large per diem staff. Usually people stay for their career, so it can be tough. The most senior folk tend to do 2 16s and an 8, and that's their full time for the week, done in 3 days.
FDNY has a lot of their info online, you can find salary and academy info easily.
The privates, places like SeniorCare, are weird. They have the FDNY computer system in their trucks, but for the most part, to my knowledge, they're just doing IFT work. They are not primary 911, but sometimes will transport if flagged down or if major stuff goes down. Their schedules vary, 8s, 12s, whathaveyou. There are a lot of these, a few in the bronx that i THINK have 911 contracts, but I'm not too familiar with up there.
Northwell (formerly LIJ) is primary 911 for some areas, though the bulk of their force is transport. So their city 911 trucks are the same as any other voluntary hospital. As far as I'm aware they make the most or second most, under Presby. Also among the hardest to get into.
They also have their own set of protocols, different from everywhere else. Some of it's good, most of it not so much. With hospitals so close all the time, they dumb it down to (less than, imo) minimally necessary. I did my paramedic internship here as well, so am familiar with those protocols too. I think BLS will be getting glucometry soon.... While even EMT protocols are different than the state, they don't require a test, only medics do. They recognize EMT and MEDIC, that's it. Some services will test you as part of the hiring process, on general knowledge, with a few protocol questions. Biggest difference that I remember is 162mg asa, not 324. They were a bit behind on the "no more backboards" update. Those things move slower there.
Ok... I tried to hit everything. Let me know if you have any more questions.