What is the difference between F-16C and JF-17 in terms of role?
Firstly, you should understand that these two fighters are from different countries (F-16 hails from the US and serves with many NATO countries, the JF-17 is a Chinese design), but were developed along closely parallel project focuses. The F-16 was developed with the advent of highly maneuverable and powerful Russian air-superiority fighters such as the MiG-29 in mind.

Designed along the inherently unstable design idea, the F-16 is pretty much the epitome of maneuverable and agile fighting machines. In addition it was meant to be produced in relatively greater numbers than its much faster, heavier, and air-superiority focused cousin the F-15. This is one aspect that it accomplished very very well as the F-16 was quickly run into mass-production via bulk requests from the USAF which, at the time, had much greater funding that it does now. The F-16 turned out as an affordable fighter that was good enough for the USAF, not too good to be banned from international export, and flexible enough to be used in a variety of roles and ensured its use well into the 21st century.

The more obscure JF-17 is a Chinese design meant to do the same thing the F-16 did when it came out. Chengdu wanted a fighter that was rather maneuverable, and was viable and cheap enough to succeed in the international market. What resulted from a joint project between PAC and Chengdu was a fighter that could compete both in real-life maneuvering and technologically with its peers. In addition at only $15 million per unit for a block 1 type JF-17 it is one of the cheapest 4th generation aircraft of its kind available. 

The two aircraft were built with similar roles in mind, and in practice fulfill them similarly as a result. The F-16 is in some ways the superior of the two, having benefited from lessons learned in many deployments around the world, but both are designed for multi-role usage, inexpensive operation, and affordability en masse.