The difference between EMTs and Paramedics isn't often highlighted in the media or the TV shows about first responders, however the difference is fairly substantial and depending on the emergency different individuals will be sent out to respond.
Many health authorities have two levels of emergency responders, the ambulance crews, and while the terminology will vary they are essentially EMTs or paramedics. The training level between the two levels can be as much as 150 hours for an EMT versus 1500 for a paramedic level individual. This has a huge difference on the types of procedures and level of care that can be provided when the ambulance crew arrives on the scene.

EMTs are typically responsible for limited emergency response care and transporting individuals to hospitals where they can receive further treatment. The response care they can provide is limited and their ability to administer any form of pharmaceuticals is also very limited.

Paramedics are trained to carry out far more advanced procedures and are also trained in administering far more pharmaceuticals to patients. Paramedics can also provide IV's and injections, which most EMT's cannot. The exact distinction varies from jurisdiction to jurisdiction but the general differences run along these themes.

Depending on the severity of a call, dispatchers will send different crews and ambulance teams to different calls based on what the expected needs are. The last thing they want is a severe emergency taking place in one location while the trained paramedics are tied up on something routine elsewhere.