Chicago is the city of Chicago. Joliet is the third largest city in Illinois and happens to be in the Chicago metropolitan area that includes places like Joliet, basically Cook County and the surrounding counties. Image below shows Kendall which Joliet spills over into from Will county and I never really considered Kendall part of the Chicago area, but YMMV. Also I would include Lake County in Indiana, yes, that's another different Lake County. If you have a Metra station (like Joliet and they have an Amtrak stop), you can probably get a train into town if you are outside of Cook County, but all of those counties have large swathes of greenspaces and suburban sprawl and a car is recommended.