ARCA is a seperate entity from NASCAR. ARCA has its own series, including sanctioning local racing, and its own truck series, just as NASCAR does.
The cars ARCA uses are the former NASCAR Sprint cup cars, but can have bodies that are up to 4 years old (meaning that the MonteCarlo and the Taurus are legal to run in ARCA).
The ARCA series also uses a slightly different engine package than the NASCAR series do. It is the same cubic inch (358 cuin.), but has a lower compression ratio to lower the horsepower.
Another difference is that ARCA is not afraid to "get a little dirty," in that they still run on dirt twice a year. Once at the Illinois State Fairgrounds in Springfield Illinois, and once at the Southern Illinois State Fairgrounds in DuQuoin, Illinois.
ARCA cars run the same speed as the Sprint Cup cars do, for the most part.
ARCA is a great stepping stone for up-and-coming NASCAR drivers, and several former NASCAR champions have been ARCA champions, including Benny Parsons, AJ Foyt, Mario Andretti, and a few others.