There are three types of convergent plate boundaries and they can be subdivided into subduction and non-subduction.
Let’s start with the easiest one for you to understand. Continental-continental has nothing to do with subduction -- In this case, neither piece of crust is dense enough to subduct. In other words neither piece of crust can sink, or push the other to sink, so they have to run into each other head to head. Lots of folding and faulting occurs in this case along with earthquakes. The Eurasian Plate and the Australian-Indian Plate collide into each other and form the Himalayas.
OK we are done with the non-subduction. The other two types will involve subduction. To explain subduction, imagine you have two plates running into each other, and the denser plate will dive below the more buoyant one. As it gets deeper into the mantle, it melts and creates a new magma. For Oceanic-oceanic, that’s one oceanic plate collides with another oceanic plate. In this case one plate will always be denser than the other, and the denser one will subduct. As the denser crust gets deeper into the mantle, it melts and creates a newly melted magma and rises to the surface, and pokes through the ocean floor as a submarine volcano. Continuing eruptions will form a larger seamount. More and more eruptions will eventually create a "dry" volcanic island which will just continue to erupt and build as long as it has a magma source. As long as subduction continues, there will be no shortage of magma.Because all of this is happening along an entire plane, you get more than one volcano; you end up with a volcanic island arc chain of volcanoes. Good examples are the Pacific plate subducting beneath the Philippine plate to create the Marianas, and the Pacific plate subducting beneath the North American plate to create the Aleutians.
Oceanic-continental happens when an oceanic plate collide with a continental crust and the oceanic crust subducts. The oceanic crust is denser compared to the more buoyant continental crust so it subducts (sink below the other). When the magma rises to the surface, they immediately create dry volcanoes. The type of volcano created will often be stratovolcano / composite volcano, which can be extremely dangerous. Good examples are the Juan de Fuca plate subducting beneath the North American plate to create the Cascades, or the Nazca plate subducting beneath the South American plate to create the Andes.
Summing up, so if there’s no subduction involve, then there’s earthquake; when there’s subduction, there will be volcanoes forming.