Mostly right, except for saying EMTs essentially function as an assistant.
EMT have much more basic training and they make like 30K a year. Their training is usually between 100-160 hours.
Paramedics
have a ton more training, closing to 1200 hours, and as you said are
qualified to use drugs. They don't make too much more money a year,
closer to 40-45k depending where they are.
Just saying you hypothetically work 2000 hours a year, a EMT would be about $15/hour and a paramedic would make $20-23/hour.
But
a lot of places run EMTs & paramedics at the same time. They both
respond and do the same (generally) job. One is just able to respond in a much completer fashion than the other. I guess I just wouldn't say EMTs function primarily as an assistant to an paramedic. Lots of times there are no paramedics around, just the EMTs. Depends where you are/how busy the area is, though.
Just to add, I guess, I think all firefighters must have completed their EMT-basic and the ambulance crews that work for the fire department are all paramedics. I think something like 90% of fire department calls of medical emergencies.