What are the differences between a car battery and other smaller batteries?
The difference is chemistry, and size. A 9V Battery is typically an alkaline battery made up of 6x 1.5V nominal cells. A car battery is typically a lead acid battery made up of 6x 2V cells or piles.

Lead Acid cells are bigger, heavier, and designed for high current over short time applications. Their chemistry is very dangerous or corrosive to humans and not well suited for consumer use. Sulfur and brimstone. 

Alkaline batteries are better at low current over a longer time, weigh less, and are generally safe even when leaking. It won't eat through you like sulfuric acid would. Perfect for consumer products. You could get 12V alkaline batteries, like for garage door openers, but the capacity is low. All those batteries are, are multiple single 1.5V cells in series. 9V batteries sometimes have multiple AAAA sized cells inside. Smaller than AAA cells.