It's important to note that "Inca" refers to both the ruling class and the empire itself. Quechua was the official language of the Inca Empire and was spoken by a vast majority of the population.
There are actually several varieties of Quechua, with the most widely spoken being Quechua A or Classical Quechua. It is still spoken by millions of people in South America, primarily in Peru, Bolivia, Ecuador, and parts of Argentina and Chile.