No. EMT-B is the level of certification. The 'B' stands for 'basic' and that is the level of care you provide. Paramedics (EMT-P) are trained in Advanced Life Support (ALS) There is another level valled EMT-Intermediate (EMT-I) which is not found in all areas. EMT-I's can start IVs and perform other skills that basic EMTs can not.
You can volunteer or be paid as an EMT. Paid positions for 911 services are often at the paramedic level; it depends on what type of service is in your area. Many cities and towns have integrated fire/ems departments and their personnel are Firefighter/Paramedics or Firefighter/EMTs. In other areas Fire and EMS are completely separate. Here in CT many paid services have ALS rigs with one EMT and one Paramedic - as the EMT you drive the rig unless it is a very basic call. They also have BLS units which have two EMT-B's In this area it is not hard to find a job as an EMT-B, but the pay isn't very good and you may get stuck driving the rig all the time or only doing BLS calls. Another option is to work as a ER Tech after you get your EMT-B.
I have been a volunteer EMT for 18 years - 14 as a basic and 4 as an EMT-I. One nice thing about volunteering is that most volunteer services do only 911 calls. Not that all 911 calls are true emergencies, but you are less of a taxi service than many of the paid service rigs. There are paid services that also only do 911 calls - it depends on the service agreement they have with the city or town.
Call around to the various services in your area and find out how the EMS system operates. Ask if they are paid or volunteer, city or private service employees, part of the fire services or separate, and where can you take a class in the area. The EMT-B class is about 120 hours plus some ride time and state and/or national certification exam (written and practical).